After looking for some guide to all the bonus objective from the DLC, I couldn't find any complete one, so the 100% completionist in me had to poke and look around the mission files in the editor as well as follow the findings of a few other people.
Not everything in this guide might not be 100% accurate when in come to things like amount of casualties allowed and turns count, this is still a WIP.

About objectives that give you bonus units in the same mission as the objective themselves: Their triggers happen at the beginning of the next turn but victory conditions are checked at the end of the turn.
This mean you must not complete the bonus objective and the main objective in the same turn or the mission will end before you get the units.

Mission 1: Stygies River Bank
Objective: On turn 9, steel legion infantry spawn in the northeast corner of the map. You just need to keep them alive

Advice: Really easy. Even without any support, just keep the infantry on a building and the orks will usually fail to kill them before the gunship spawn. You should send support anyway since gunships are glass canons and it could be destroyed after it spawned.

Reward: On turn 11 a vendetta gunship is spawned near the legion infantry spawn location.

Mission 2: First Strike
Objective: On turn 2 a bunch of guardsmen and heavy bolter devastators spawn on the small northern island. You need to keep the guardsmen alive.

Advice: Just keep the guardsmen were they spawn, on cover in front of the devastator so they'll be protected by fire support.
Meanwhile get some of your units north to take care of the enemies at the east of the small island they're not too dangerous to your troop but will kill the guardsmen if they reach them (they usually don't reach them before the basilisk spawn).

Reward: On turn 5 a basilisk armageddon pattern spawn in the swamp spot of the northern island.

Mission 3: Stygies Defence
Objective: You start the mission with 2 guardsmen and mortar support on 3 victory hexes in the north east of the map. They must survive.

Advice: It's best to split your troops anyway for this mission, some on the central island, and other going for the north island.
There is multiple gretchins with a size of 90 to the west of the victory hexes that will make a beeline for them, so have your guardsmen fall back (and have the mortar protect them with fire support.
If you have transports, your squads can easily reach the guardsmen on turn 1.

Reward: On turn 6 a Banesword spawn near the eastern road exit.

Mission 4: Chaos at Tartarus
Objective: More than 20 steel legion units must survive

Advice: Make sure you have a good amount of fire support unit (thunderfire canon are fairly effective on this map as you don't really have to move).
You need to spread your unit across the map while focusing on taking out the three pockets of orks inside your ranks: the dreads in the center (use your own dreadnoughts) the grot mega tank north and the warboss on the east.
It's better to reinforce the guardsmen to make sure they don't die rather than attack as low moral guardsmen aren't very good anyway.
The steel legion on the southern hex tend to not survive long enough but you can still have plenty enough units.

Reward: On turn 7 a scout warhound titan spawn on the eastern edge of the map

Mission 8: Hive Volcanus Assault
Objective: As you get close to one of the hive access ramp a message will pop up requiring you to kill the ork slaver. It is a nob squad strength 50 in front of the topmost hive ramp.

Advice: You'll need to be fast as a whole, as this mission has a fairly low turn limit. You can cut short through the cliff but only infantry can get through.

Reward: A baneblade and a stromblade (both upgraded) spawn on the west edge of the hive.

Mission 1: Acheron Intervention
Objective: Still unsure about this one. Even if you only have the 7 objective hexes in the trenches and the city up north, the bonus unit still appear, it might be tied to casualties.

Advice:

Reward: On turn 9, a macharius vulcan appear in the hive.

Mission 2: Depths of Archeron
Objective: Keep control of all of the objective hexes

Advice: Hurry to protect the southeast objective. Make sure the militias and ogryns surround the sabre platform so they can get fire support. Reinforce auxiliary squads if they risk being eliminated.
Getting close to the center of the map trigger a large ork force, so don't move in until you've cleared the south and you're ready to get all your troop up.

Reward: Wyvern spawn near the southeast objective

Mission 3: Holding Hades
Objective: Keep control of all of the objective hexes

Advice: You really need to know how to use fire support and to alternate your troops on the front line so you can keep fresh unit in the front and heal the ones in the back. Keep as much of your units in cover and prevent the enemy from reaching it to ensure maximum damage.
The enemy attack in waves, so take advantage of moments of respite to rest and reinforce.
This is one of the missions were thunderfire canons are quite good due to their range.
The bulk of the enemy attack the center with lots of heavy units so keep some dreadnoughts and antitanks here. Keep the mortar auxiliary safe behind other units, they are very effective against large squads.
For the northeast hexes the enemy comes from the south and west. You can bottleneck the enemy in two spots: the pillars south and between two hallways west. Mostly infantry come west while a large amount of dreads followed by infantry come from the south.

Reward: Shadowsword (weapon upgrade) spawn at the northeast end of the road

Mission 1: Archeron Landing Zone
Objective: Keep control of the blood angel objective until turn 10 and have no more than 1 blood angel squad wiped out (this include the drop pod).

Advice: The challenge here is that the orks attack from north and south and the blood angel just won't survive by the time your ultramarine get through the orks in the center.
The solution is to keep the guardsmen alive: leave their mortar on fortification and surround it with the other steel legion units. You'll probably lose a conscript squad but you'll have enough to keep the mortar safe and now every ork coming from the north will get hit by mortar fire support when they try to kill the guardsmen.
If you keep reinforcing them and softening the healthier orks with mortars (don't try to take out the central ork artillery, just replace the casualties), the steel legion should manage to hold the line fine and the blood angels will take care of the orks on the south, leaving ample time for the ultramarine to clear the center and face the heavy units that eventually come from the south.

Reward: Mission 3 on turn 6, several blood angels appear and join your army (2x death company squads, 1 sanguinary guard, 1 baal predator, 1 whirlwhind, 1 Assault bike squad)

Mission 2: Road to Hades
Objective: On turn 4, enemies on the east side of the river will move to capture your starting point (Aurtulo will issue a warning). Kill most of them to get the objective (Autrulo will announce it).
The enemy force is composed of: 6x biker mob, 2x grot bomb launcha, 7x commandos in truk, 3x mega dread (one of each variant), 1 skullhamma battlefortress.

Advice: This is possibly one of the hardest bonus objective as you're still lacking strong resilient units and this objective require you to split your forces. It might take many tries until you get the right balance. Don't hesitate to discard terminators and assault marine and go heavy on dreadnoughts, they're hand down your best units.
Another issue is the composition of the enemy group. You'll need good anti infantry to kill all of the bikers and commando, but you also need heavy units to take out the battlefortress and mega dreads. I recommend at least 1 dreadnougth hellfire, 1 sternguard squad and 1 heavy bolter devastator as well as the Land speeders and snipers auxiliaries.
Yet another obstacle is the terrain, with lots of forest slowing down your unit and preventing them from quickly joining up with your force to help on the main objective.
I suggest to move your chosen units north of the trenches at your starting point and clear the few gretchins before settling. Ignore the enemies in the big central forest as it just take too much time to clear it. The moving enemy force will try to go around you if possible so try to block their path and use your snipers to kill anything that get trough to minimize time spent. As soon you get Aurtulio's confirmation, get your unit moving to the main objectives.

Reward: Mission 3, the ork force flanking you from the east will have no vehicles (battlefortress, big track, bikers and deff dread) and no mega armored nobs.

Mission 4: Walls of Tartarus
Objective: Keep control of the salamanders' objectives until turn 7 and have no more than 1 salamander squad wiped out.

Advice: The salamanders units are few and not very good, they won't last long without you.
Split your army in two, one on the south-west to crush the orks there as fast as possible and get the salamanders west side safe.
You can ignore the north-west objective at first since the enemy taking it will just stay there.
Put your other units north of the salamanders to try to control the somewhat open area to the right and clear the ramp going south. Send a few units to assist the salamanders on the east side if needed until your southern force go through the bridges and relieve the salamanders.
Replace salamanders losses if they're at risk of being wiped out.

Reward: Mission 6 on turn 3, several Salamander appear in the narrow passage north of your starting point and join your army (1 whirlwind, 1 upgraded vindicator, 1 venerable dreadnought, 1 tactical squad with grav gun, 1 fire drake squad, 1 devastator with multi melta squad)

Mission 8: Volcanus Mountains
Objective: Kill all enemy units in the south-west depot

Advice: Send a force along the south edge to reach the depot. You'll need dreadnoughts to deal with the gargant and stompa (Sanguinary guard is surprisingly good in melee too).
Since a road from there lead to the north, you're not actually wasting much time compared to the rough terrain elsewhere.
The approach is a bit tricky as cliff are in your way. Beware the warboss with his sight of 4.

Reward: Most of the gargants in Mission 10 while be gone (about a dozen)

Mission 9A: Walls of Death Mire
Objective: After taking out the ork defending the bridge near your spawn points, refugees will appear. 4 squads of refugee or more must survive until turn 6.

Advice: Not too hard. Apart from 2 lootaz, the refugees are threatened by a bunch of warbikers but they'll tend to block each other. The other enemies on the east tend to be out of reach.
Just move your units south and have the refugee fall back west but make sure they don't end up blocking the way for your other units.

Reward: Mission 10 a large detachment of Salamanders will appear south.

Mission 9b: Death Mire Assault
Objective: Clear out all ork in the southwest area.
Watch out! If all orks are dead you win regardless of objectives, but the victory trigger happen before the bonus objective one. So make sure to leave some orks alive outside of the bonus area until you receive the message of confirmation from Aurtulo

Advice: You're gonna have to use more than the few blood angels for that as this is probably the most well defended area of the map, partly due to the large amount of cover.
There is a lot of mega nobz and tankbusters so even dreadnought and land raider may take a beating. Sniper, indirect units and melee units will be needed.
Make sure to check every corner, there's a bunch of enemies just sitting there, endlessly reinforcing.

Reward: Mission 10 a large detachment of Blood angels will appear south.

Only one mission of the DLC has a bonus objective

Mission 4: Inquisitor's Request
Objective: Kill all enemy units

Advice: Fairly easy. Most of the enemies either sit on objectives or will move to engage you when you're spotted. The only units that you might have trouble to find are :

• A tarantula turret north of the small western bridge
  
• A sabre turret on the eastern ramp (next to a devil dog)
  
• A deathstrike north of the western hive objective

The Inquisitor will congratulate you once you take out the last enemy. Otherwise he will say he's disappointed in you.

Reward: In mission 6, a few turns in a Banewsord, a Stormblade and a StormLord (all upgraded) appear south of the trenches.