This level contains 8 secrets and a super secret.
1/8 - Before going through the hall that leads to the underground tunnels, take the opening to the left and turn around to come across a stash under the structure. (Shotgun Slaughter III)
2/8 - Following from the previous secret, get on top of the wooden fencing next to the tunnel entrance via the pillar nearby, walk on to the other one, turn around and jump-dash to reach another stash consisting of some ammo and two health packs.
3/8 - Before dropping down into the second hall in the tunnels with the purple crystal, jump-dash onto the surrounding ledge and follow it all the way around to its end. Use the slightly protruding part of the wall to uncover an armor and two health packs.
(*) It might be better to check the super secret at this point, rather than backtracking for it later.
4/8 - Past the purple gate, battle it out till stumbling upon a chasm deeper into the tunnels. Once there, use the indented wall between the two torches on the right to reveal a hidden passage containing some ammo and two health packs... as well as a curious handle on the wall.
5/8 - Before dropping down from the red keycard balcony, jump-dash onto the roof across and turn the corner to find some more ammo.
6/8 - Following from the previous secret, climb the ladders found on the same alley and drop down into the structure from the opening at the top. After looting the place, instead of leaving via the door, destroy the crates to its right, get into the opening and jump-dash over the beams to discover a hidden room. (Inferno Gauntlets Slaughter)
7/8 - Following from the previous secret, climb the ladders once more, turn right at the top this time and reach the ledge of the central tower via the wooden fencing next to it. Follow the ledge and jump-dash onto the roof of the abode at the corner. Once there, destroy the wooden panel on the roof and drop inside to find yourself in another hidden area. (Katana Mutilate II)
8/8 - Before using the red keycard, explore to the right looking for a sand tunnel with a cracked wall at the end. Destroy it and hop into the teleporter at the end of the path to reach the side area. Once on familiar ground,[counterstrike.fandom.com]battle it out to the end of the underpass and use the differing part of the wall to reveal a hidden compartment with some ammo and two health packs. 'No Payne, no gain.'[www.mobygames.com]
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SUPER SECRET - The activation of the fountain nearby the central tower requires four handles to be turned, which are all located in the tunnels beyond the purple gate. Starting from the save point down there, take a right and shoot the first lever found at the corner of the room to get the water flowing. Down the next stairs, use the second handle found on its side to keep the flow going. Get into the passage from secret #4 and use the third handle found within. Turn the corner of the U-shaped hallway after the chasm and shoot the fourth handle hanging on the wall. An on-screen message appears: 'A fountain's rune is activated.'
After that, return to the alley to find the fountain glowing blue. Use it to unlock the door to the adjacent abode and get the goodies. (Hurricane -G- and a Blood Gem)
(!) The achievement gets unlocked the moment Templar states that he found a super secret.

This level contains 7 secrets and a super secret.
EXTRA - Once inside the first structure, destroy the cracked part on the wall to the right to find the teleporter to the side area. Survive the arena fight within to unlock the stash that consists of a rune (Blast -G-) and a blood gem.
(!) The achievement gets unlocked the moment Templar emerges victorious from the fight.
1/7 - Back on the main path, step out of the structure and check the corner to the right of the sandfall. Use the wooden panel on the ground and drop down to discover a stash. (Black Bow Expansion III)
(*) It might be better to check the super secret at this point, rather than backtracking for it later.
2/7 - After getting out of the underground tunnels, clear out the structure you find yourself in and use the wall above the tomb next to the save point on the second floor to reveal a compartment with a rune, an armor and some ammo inside. (Pistol Expansion III)
3/7 - Following from the previous secret, right after taking the teleporter to the other side, turn around and jump-dash to the ledge across to find a cache around the corner containing lots of heavy ammo, three health packs and some SMT energy.
4/7 - Following from the previous secret, ascend the stairs leading outside, turn around and look for the indented part of the wall at the corner. Use it to reveal a side hall with more ammo to fuel your carnage.
EXTRA - Following from the previous secret, explore beyond the sandfall at the corner before moving into the next structure to find an armor and lots of heavy ammo laying out in the open.
5/7 - Following from the previous secret, continue into the structure, cross the chasm and use the indented part of the wall signified by a torch between the crates to find some heavy ammo and two health packs. Surely you remember the first RTS game of all-time,[www.mobygames.com]no?
(*) Credit goes to Lampenpam for recognizing the crest of Harkonnen House.
6/7 - Upon arriving at the palace, jump into the space between the legs of the statue on the left and use the indented part of the wall to open up a hidden compartment.
7/7 - In the structure that houses the red keycard socket, a rune can be seen residing on a ledge above. Get onto the vase at the corner, then hop onto one of the pillars by the housing and jump-dash from the end of the thinner ledge to reach it. (Inferno Gauntlets Expansion II)
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SUPER SECRET - A tablet needs to be pieced back and returned to its designated place next to three others to uncover a hidden treasury. If backtracking, start by stepping onto the rune formation in front of the palace to reveal a path back to the other side. Get the first piece from the backside of the tomb with a skeleton laying on it found in the underground tunnels (just before secret #2). Grab the second piece from the similar tomb located between the stairs out of the tunnels and the exit (secret #4). The third tomb, thus the final piece, is found in the next structure, right around the corner (secret #5).
After collecting all three, return to the first structure that also houses the teleporter to the side area. Mount the completed tablet where it belongs to reveal the hidden room right by. (Boss Killer -G- and a Blood Gem)

This level contains 7 secrets and a super secret.
1/7 - Before going up the slope in the initial cavern, check the opening next to the torch at the very end to find some heavy ammo between the stone blocks.
2/7 - Following from the previous secret, continue up the slope and and drop down to the ledge below the two health packs on offer (not on Nightmare) to pick up an out of sight armor.
3/7 - Just before going through the stone gate, explore the opening to the far right to discover an armor, some ammo and two health packs hidden around the corner.
4/7 - Turning the first corner past the gate, look for a duo of stone blocks to the left and utilize them to reach the ledge above. From there, turn around and jump-dash to the armor residing on another ledge across.
5/7 - Following from the previous secret, cross the bridge over the chasm and check the area to the left of the purple gate to find the differing part of the wall around the corner. Use it to open up a compartment with an armor, some ammo and three health packs inside.
(*) Note that even if you get dropped down right here later through normal progression, I think the goods inside serve their purpose better as earlier options.
6/7 - Just past the duo of pillars in the underground ruins, take the steps down to the right and follow the ledge around to find a hidden rune and some heavy ammo. (Shotgun Expansion III)
7/7 - Following from the previous secret, take the path that can be seen below on the other side of the stairs and destroy the cracked wall in the next room to reach the side area. As soon as you step into the cavern beyond, look for a ledge below on the right and drop down to find another hidden rune and an armor. (Katana Focus II)
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SUPER SECRET - As soon as you are teleported back from the side area, drop down to the path that takes you its entrance once more. From the corner of the walkway, jump-dash towards the sandfall that strangely stops halfway in the air. A platform emerges and lifts you upwards, revealing a second sandfall nearby. Utilize it in the same manner to reach the highlighted ledge on the other side. Once there, use the indented part of the cavern wall to reveal the hidden room of goodies. (Combo Shoot -G- and a Blood Gem)
(!) The achievement gets unlocked the moment Templar states that he found a super secret.

This level contains 9 secrets and a super secret.
1/9 - Upon arriving at the first junction, check the dead end to the left and use the part of the wall next to the support with an unlit torch on it to reveal an alcove containing an armor and some heavy ammo.
2/9 - Taking a right at the intersection on the second floor, jump on top of the minecarts to your left and crawl through the opening behind them to find another alcove housing assorted ammo.
(*) Check the super secret at this point, otherwise you are pretty much locked out of it.
3/9 - As soon as you reach the third floor with the help of the minecart, turn around, jump-dash to the ledge across and use the indented part of the cavern wall to discover a cache. (Black Bow Slaughter III)
4/9 - Following from the previous secret, return to the third floor, destroy the crates next to the cart on the right and drop down to grab the armor and the ammo from the ledge below.
5/9 - After taking the elevator to the fourth floor, go right towards the other one that takes you back to the first floor and jump-dash to the platform hanging across. From there, hop onto the adjacent walkway and use the part of the cavern wall next to the unlit torch to reveal a hidden alcove.
6/9 - Following from the previous secret, jump on top of the long minecart at the side of the next intersection and turn around to come across another alcove. (Trap Launcher Mastery III)
7/9 - Following from the previous secret, jump-dash towards the tunnel to the right a little ways onto the tracks and destroy the cracked wall at the end to reach the side area. Before taking the cart for a ride, use the cavern wall below the torch to the right to uncover yet another hidden alcove.
(*) The ride is pretty tricky and may require multiple tries. So save here to not lose progress. Sniper Shotgun rune coupled with a full bar of SMT does wonders, just so you know.
8/9 - Back on the main path, drop down to the ledge below the slope that leads to the next elevator to reach another alcove full of supplies.
9/9 - Once you reach the yellow keycard pedestal, use the wall between the pillars on the opposite side to discover a side room. (Inferno Rocket Expansion III)
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SUPER SECRET - Well, this one must be the most 'out of the box' super secret of them all. There is a hidden room right above the tracks that the minecart travels after you pull the relevant lever down, yet it is out of reach by normal means.
Guess what? The trick lies in skipping the related cutscene!
In preparation, open the door that leads out of the room and get the energy laying around to fill up your SMT bar. Since this is a one-shot affair, it is a good idea to save the game at the provided point too. So pull the lever down, go into slow motion right after skipping the cut, make haste to get on the cart as it is on its merry way and climb the ladder as you pass under it to finally reach the alcove with the goodies. (Just a Measly Blood Gem for all that effort)
(*) Kudos to KivesSilta for figuring this one out.
Turns out it is also possible to get on the ladder in question by simply jumping towards it, without help from the cart (as stated by Sircookie, Mesarthim and Pekrosha in the comments) yet I could not manage to do so no matter how many times I have tried. Still, since nearly all of the super secrets are more or less puzzles in themselves, I think the intented way of getting this one is rushing after the cart on its way, as described in the previous paragraph.

This level contains 8 secrets and a super secret.
1/8 - After dealing with the welcoming horde, turn the lava covered corner nearby the first titan to come upon an assortment of items.
2/8 - Following from the previous secret, turn around as you pass through the opening and jump on top of the stone blocks to reach the stash on the other side. (Trap Launcher Expansion III)
3/8 - Continuing along the shoreline, jump-dash around the outer wall by the third titan to discover another stash waiting by the other side. (Templar Rush III)
(*) It might be better to check the super secret at this point, before snatching that armor that can be seen on the platform rising from the lava pool in front of the central temple.
4/8 - Following from the previous secret, pass through the stone gate, turn right and drop down to the ledge in the lava next to the fourth titan to grab yourself more ammo.
5/8 - Move along the shoreline deactivating the crystals by the fifth and sixth titans. Once you reach the seventh and the final titan, take the slope down to the right of the crystal and jump-dash to the ledge in the lava to get the goods laying out in the open. (Pistol Rush III)
6/8 - Following from the previous secret, destroy the cracked part on the rock formation found right across the last crystal to reach the teleporter to the side area. Jump in, battle it out to the very end and use the part of the cavern wall between the two spikes just below the exit teleporter to open up a hidden cave. (Inferno Gauntlets Slaughter II)
7/8 - Returning from the side area, move towards the central temple and check the opening covered by flowing lava to the right of the stairs leading to it to find a stash around the corner.
8/8 - Following from the previous secret, find the opening next to the tower at the back of the temple and take it to discover another stash. (Katana Slaughter II)
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SUPER SECRET - Before grabbing the armor residing on the platform rising from the lava pool in front of the temple, look for a lever on the pillar right next to the said pool. Pull it down, wait
around five seconds and pull it back up to turn the armor into a smoking-hot unique one, just like the one found back in E3M2: Dead Sails - only to protect from the lava damage this time.
Don the armor, dive into the pool and swim through the opening found in the corner towards the sixth titan to find yourself in the hidden cave of goodies. Note that it is still possible to swim through the lava without the protective armor. In that case, SMT comes in handy to reduce the damage taken during the rather long swim in the tunnel. (Cerberus -G- and a Blood Gem)
(*) Credit goes to Schneekanonenschütze for finding out the armor transformation.
(!) The achievement gets unlocked the moment Templar states that he found a super secret.

This level contains 4 secrets and a super secret.
1/4 - Missable. Right at the start, turn around and drop down into the lava pool to find a hidden alcove beneath containing a rune, an armor and some heavy ammo. (Templar Toughness IV)
2/4 - Missable. As soon as the lava starts rising, hurry up the hill, drop down to the ledge on the left, grab the goods on offer and make your way back up. (Inferno Revolver Expansion III)
EXTRA - Missable. After the section with the rising lava, destroy the cracked part of the cavern wall to find the teleporter to the side area. Survive the climb up the hill beyond to reach the stash that consists of a rune (Shotgun Expansion III) and a blood gem. While there, do not forget to say farewell to your beloved T-800.[terminator.fandom.com]'Hasta la vista, baby.'
(!) The achievement gets unlocked the moment Templar mutters that he is not an ape nor frog.
(*) Check the super secret at this point, otherwise you are pretty much locked out of it.
3/4 - Missable. As the lava starts rising for the third time, make quick work of the monsters standing in your way and drop down to the ledge found to the right of the gate before the goods are fully covered.
4/4 - After deactivating the crystal, step into the following cavern and turn left to find the barely noticeable steps of rock at the corner. Jump on top of them, turn around and dash into the opening to find an armor and some heavy ammo.
(*) Note that there is no going back once you drop down to the arena.
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SUPER SECRET - A missing book needs to be saved from the rising lava and returned to the hidden library within the mountain. Just after surviving the second lava rush, turn around to see a skeleton laying on one of the spikes in the distance. The spike nearest to your location has a ledge by it. So start from there and follow the pretty much laid out path over the spikes to reach the skeleton in question and grab the book from his arms.
Continue on, survive the third lava rush and dive into the lava pool beyond the save point thereafter. Once you resurface in another tiny library, put the book back in its designated place to reveal the goodies behind the shelves. Do not forget to get the book page on the floor before leaving via the teleporter, as it serves as the fourth and the final part of the campaign-wide 'mega' secret. (Roar -G- and a Blood Gem)
(!) The achievement gets unlocked the moment Templar states that he found a super secret.
(!) The achievement gets unlocked after Templar defeats the boss.
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Keep on exploring in the fifth and the final episode: