Achievements were added to the game in version 1.7. It looks like recent anniversary update, besides totally ruining the game, also broke all achievements.

To still be able to unlock all achievements you need to select "version170" beta version in game properties. This is the last proper version of the game and the one where the achievements were added.

Real Friends
Played a four player game


This is an achievement which you can actually get without playing much at all. All you need to do is going in versus mode and selecting any 4-player level. As soon the level starts, you get this achievement.

The Secret
Found all 48 secrets in Gish


This one is not a very easy one, but you can get a game over screen and you don't need to do this in one sitting, although it must be done in a single playthrough. Some secrets are easy to find, some are real mystery.
I am not going to post every single secret, there are some guides already avaliable in the net. The one on gamefaqs[www.gamefaqs.com] is pretty good, i personally used it.
You will get the achievement at the end of the 5-4 when you get to scoring screen.
You also must avoid any secret levels or warps. Even if you find all the secrets in a level, but finish it through secret exit, it will not count.

Thanks to steam user Cos for some testing with this achievement.

Super Gishio Brother
Found the Mario level


This one is quite easy. You need to find a hidden 1-2 Super Mario Brothers level. The secret itself is located in level 1-3. After you climb the wall with a spike on one side and slide down through the narrow passage, you will end up near a platform hanged on 2 ropes.
The secret is located right below the spike pit. To access it, carefully (or not - health loss will be no major, plus you don't need health, as the level will finish when you touch the secret) climb below left static platform and use your weigh to crush 2 leftmost spikes.
Go down the hole and you will see a ? block from SMB game. Break the block and move gish on the space where it was and you will get to that level.
Achievement will unlock right after you touch the area and finish 1-3 level with that.

Explorers Club
Found the Pitfall level


This one is located in 2-1. Not far from the start you will see a vertical platform that is "supported" by the breakable block. The platfrom would act like a bridge if it falls to the right. Instead, stick to it and topple it to the left and fall in the gap. You will find some coins and a secret notification. This is not all. The middle block is breakable. Climb up and use HEAVY to break it. Slide down through the passage and you will find big 8-bit sprite. Touch it and you will warp. Achievement will unlock soon after.

Happily Ever After
Rescued Brea


SImple one. Get to the end of the game. The last level is 5-6. Fight Hera until you manage to make her drown into lava. This can be done in following steps:
1) Make Hera fall onto platform below.
2) Push the right switch to open passage into lower level.
3) Briefly jump down and get back up onto middle level so that you can see lowermost level.
4) Lure Hera onto thin platform to the right.
5) Difficult step: slowly move left when Hera is positioned on left part of platform mentioned above. As there is 1-block high wall and Hera cannot climb well, she will most likely not be able to climb it if you move slowly.
If you managed to do that, go to the left upper part and hold the button there for about 5 seconds. If Hera is alive - repeat. If you can't make it work - proceed to step 6).
6) You need to manage take a block in the lower left and shoot it into upper left. This is pretty hard with Hera. Try to use right lower part as an "obstacle" for Hera. She climbs poorly. When you do this, lure Hera into lava. A path to Brea will also open.

After Hera is dead, you need to proceed into right lower part. When you get there, Brea will all of sudden fall down along with its cage.

To get Happily ever after, you must prevent Brea from falling into the lava. Position youself in such a way so that you will be able to touch the cage when it falls but at the same time have enough surface in ground so that cage does not pulls you with it. Then hold stick button and catch Brea. After that just move left. Achievement will trigger in the last cutscene.

Crappily Ever After
Didn't Rescue Brea


SImple one. Get to the end of the game. The last level is 5-6. Fight Hera until you manage to make her drown into lava. This can be done in following steps:
1) Make Hera fall onto platform below.
2) Push the right switch to open passage into lower level.
3) Briefly jump down and get back up onto middle level so that you can see lowermost level.
4) Lure Hera onto thin platform to the right.
5) Difficult step: slowly move left when Hera is positioned on left part of platform mentioned above. As there is 1-block high wall and Hera cannot climb well, she will most likely not be able to climb it if you move slowly.
If you managed to do that, go to the left upper part and hold the button there for about 5 seconds. If Hera is alive - repeat. If you can't make it work - proceed to step 6).
6) You need to manage take a block in the lower left and shoot it into upper left. This is pretty hard with Hera. Try to use right lower part as an "obstacle" for Hera. She climbs poorly. When you do this, lure Hera into lava. A path to Brea will also open.

After Hera is dead, you need to proceed into right lower part. When you get there, Brea will all of sudden fall down along with its cage.

To get Crappily ever after, you need to let Brea fall into the lava. Achievement will unlock when you get to last cutscene.

Jesgish
Found God mode


Easy to find, hard to get.
This one is in 5-1. You need to get into balcony secret first. This is hard to do, because you will frequently fall off the platform or just die from compression.
Once you get there, there is a hole in the ceiling. Look at the screenshot:
Follow the hole up and the to the left. You will end up here:
Touch the box and you get God mode - and its achievement. God mode allows you to drag dynamic objects like enemies or block around with your mouse.
It should be noted that this mode is very useful when going for Ludicrous difficulty, althrough i did not use it.

Hell and Back
Made it through Hell without dieing


This one is pretty tough. I can only say that practise rulez. Or... bad programming does.
You can unlock this achievement in the following way:
Go to the Isle of death (see related achievements), get to the Satan then EXIT the game when you are on screen that allows you to start 10-5 or return to menu. THen simply start the game and join the Satan. I accidentially got this achievement in such a way.

You can always go fair way. I suggest SMB secret level warp to 3-1 to get faster to hell if you die.

Satan Slayer
Defeated Satan


Follow instructions in "Sympathy for the Devil" to get to the Satan.
When you get to him, reject to join him.
Now, you probably expect lots of figthing strategy to be written here. However the Satan is in fact a regular mob, it just have horns. So you need to simply stomp/crush him just like regular critters. You will get achievement shortly after.

Sympathy for the Devil
Joined Satan


1) You need to get to level 3-4 on any mode.
2) Go to this location (right before shooting skull pillars):
What you need to do is to stick to the first pillar so that it carries you high up. Then you need to stick to some surfaces there. You will notice 666 platform to the right.
Touch it and warp to secret level Isle of the Dead.
3) You must complete this level. If you die, you get back to 3-5. General advice is speed: tarballs that are located here and there are NOT worth taking unless they are on your way. You should get there pretty intact. Main rule: do not panic if you are being attacked by the ghost.
User "432 Hz" made a video on completing this level. Please notice how the stick button is used - it is tapped instead of held, which allows for more speed than normal moving or climbing. Also notice that a lot of damage was received, but focusing on felling pillars and moving through enemies left more than enough health to finish the level.
4) You will now face Satan. It offers you to join him. Accept the offering and you will get the achievement when you get back to 3-5. You will also receive eternal life - basically its just unlimited lives. Note that these work on Ludicrous mode unlike regular 1-ups.

Ludicrousity
Beat game on Ludicrous mode


Probably the hardest achievement. You need to complete the game on hard difficulty first to unlock ludicrous mode. After that, you need to complete the game on ludicrous difficulty. That means no deaths AT ALL. Noone cares that you took 1-up, its a game over if you die.

You can find quite a lot of strategies on how to complete the game in the net. I will provide just a short description of each level.

1-1) What? You need a guide how to beat this level? Are you totally sure you want this achievement?
1-2) When you get to the boulder, go over it and down the path that it would block if it rolled down. This saves some time, and you will probably need to restart because you will die in some later levels, so saving time in earlier levels is good.
1-3) Nothing to see here.
1-4) OK, we are NO way going to go to hell, are we? Hell is difficult as... hell. So... what to do? Use a shortcut! Immediately as the level starts - and preferably just before it does, hold LEFT+HEAVY+SLIDE. This will allow you to get under a door. Now, when you are under it, release all buttons and quickly hold RIGHT(!)+SLIDE. Door's friction is still bigger than floors, so you will get propelled left. Then hold heavy till you warp.The warp leads to 4-3. WHOA, we just skipped 19 levels!
If you fail to succeed, restart the level. On version 1.7, you no more lose a life for this.
4-3) Push RIGHT boulder to the LEFT. That way is much easier and safer. Down there, use a mummy to push the button. This allows to complete this level very quickly.
4-4) Before second lava part, there is a shortcut. See screenshot:
Break blocks there, and you will avoid the chance to take a lava bath.
4-5) You don't need a boulder to break the wall. Just stick to it and press heavy when most compressed and it will break. Not that much of anything, but may save a little time... or waste... but the boulder sometimes gets stuck in your way and it is impossible to move it.
4-6) Immediately move right as fast as possible. Boss will not be able to follow you. Drop all the blocks there in a line. Use SLIDE+HEAVY+LEFT to move them left. When you are near the boss, it will start moving. Now, you got THREE chances to hit the ceiling and kill the boss. If you miss them all, lure the boss back to the left and try again.
4-7) MAKE sure you hold JUMP when the cannon shoots. If you don't, you will die from compression, and if you use heavy, you may not make it to the other side. Ignore easy 1-up here, as you will get a game over even if you collect it and die.
5-1) Avoid first shortcut, i frequently die here due to compression when swinging. Just get to first down-narrowing. Make sure you wait for the monster below and to the left come near you BEFORE you actually slide down. Try to squash him. When you come near long block, slick above it instead of pushing it - you will pretty much get to second part of that shortcut. Wait for big monster again. Then use your speed to kill monster right before the exit.
5-2) This one is the easiest from 5-x levels. Just make sure that you don't get caught under big boulder, or it is the end of your journey.
5-3) Yes, it is a metal chain that the ball hangs onto. But even metal breaks. Make sure you DON'T use heavy while riding it. Instead, use STICKY+JUMP to hold onto it and at the same time - avoid overcompression. Also, use a shortcut below moving ladder:
For the last part, stick to the moving block and pray for God that none of those critters jumps and sticks to you.
5-4) Make sure you don't get any critters above you in first part of the level. These things EAT your health and i am not even joking. For the next part, just hang onto ceiling and go right. You will have enough speed to to reach stickable surface on the right. The next part have 2 approaches:
1. Speedy: go as fast as you can and you will jump over spikes. Make sure you hold jump all the time or Gish will overcompress.
2. Slow: go really slow and hold LEFT+UP. You should be able to hold on that slicky platform. Then jump onto right upper platform. This will allow you to avoid the monster because it will break its neck.
Then we have our hope-breaker: lava lake. It ended so many of my runs before i mastered it... You need to cover lava with block so that you have bridge. After that SLIDE+LEFT+UP actually do very good job. MAKE SURE TO SLOW DOWN BEFORE A BUMP IN THE CEILING!!! But after that, make sure to speed up and kill the monster right before the exit.
5-5) Move up quickly and then move left while avoiding that moving thing. Lure both of bosses to the left. Then move right, avoiding that thing again. Don't move too far right. Use HEAVY to press the button. Then repeat when another boss is below crushing point. Easy.
5-6) See "Happily ever after" or "Crappily ever after" achievements.

The achievement will trigger after final screen when you get back to main menu.

If you absolutely need that achievement but you cannot make it in one piece, you can use save scumming: every time you complete the level backup My documents/Gish folder. Every time you die, restore from backup. I don't recommend that however - the game is not that hard.

dart193 - author of this guide.
Cos - helped with achievement descriptions. Contributed a lot of testing to The Secret achievement.
432 Hz - offered to include his video of beating 10-4. Now you can see the level layout before dying there casually strolling through!