An Ill Omen
A Foul Creche
Daemonkeeper
Long Distance Call

These four achievements should unlock naturally as you play through the campaign to the end. You can't miss these.

Hold Your Ground
Defeat Kadex at Usa'rya
Make you you bring a team with high burst damage when you go to the craftworld mission. After Kadex comes out, focus on him and kill him. You have very limited time.

Hands-On Research
Kill 10 enemies with Inquisitor Vakir
There are three missions with Inquisitor Vakir available. Vakir has two pistol ranged attacks, just use those. The first one being the Craftworld one, the second one being the one where Kadex boards the ship, the third one being the Sacrista one where you summon Draigo. You can help her by having your knights whittle down enemies' health and have Vakir fire the killing shot. Keep in mind that her melee attacks only hit for 1 damage (which means she is all but useless in melee) and cannot do the disabling crit attacks.

Junk Banishment
Defeat Morgellus, the Corroded Prince
Harvest No More
Defeat Malathian the Harvester
A Gift Spurned
Defeat Aeger the Benevolent
Death Comes For All
Defeat Munificus the Undying
Engine Kill
Defeat Cruciatus the Generous
These are the five reapers you will face in game. However, in each playthrough, you can only meet 4. You get three of them with the Codex, but then Kadex will show up and destroy the codex. You meet another one when you go to the warp for the finale. If you want all of them, either save before attuning the codex or use save backup, do one or two of them, and then revert the save to do the others.

Standard-Issue Killer
Win the final mission without any Master Crafted equipment
Strip the levelled gear from your characters and only use the stock gear with infinite supply. Grenades and other equipment doesn't matter. Make sure both squads have stock armor, stock ranged weapon and stock melee weapon. When in doubt, do it on the easy difficulty.

Executioner
Execute an enemy.
As you are forced to play the tutorial the first time around, you should be able to unlock this achievement a few minutes into the game. If you somehow skipped the tutorial, you can do an execution by knocking an enemy off balance by melee striking it repeatedly. Once they are on the ground, do an attack and the execute prompt will show up.

Exterminator
Execute 50 enemies
Repeat the process 50 times. The Librarian class has a shriek ability that can be very helpful as it can AoE mass stun enemies. You should be able to unlock this achievement before a campaign is over.

Watch Where You Step...
Kill an enemy by knocking it back
Either knock an enemy into a hazard that will kill it or knock it off the map in some maps which will instantly kill them. Purgator class has the "kick" melee skill that allows you to knock enemies back. Some melee weapons can also knock enemies back.

Look Over There!
Disrupt an enemy's Overwatch or Suppressive Fire
Frag Grenades can knock enemies away from their original location, this should disrupt their OW or suppressive fire.

Not So Fast...
Kill an enemy with an Auto
Melee classes has the "attack of opportunity" auto that triggers when enemies move by them. This should trigger the achievement.

Blood for the Blood God!
Kill an enemy with the Bleed Affliction
Either use a weapon that can cause bleeding, an Apothecary class character with the "bleed" biomancy skill or just crit strike that afflicts bleed. Get their health down to 1-2 first and pop this on them. Make sure they die to the bleeding. Also, the bleeding kicks in at the end of the enemy's turn, so plan accordingly.

Purging Spree
Kill 5 enemies with the same knight in a single turn
Grenades, incinerator, the Interceptor class teleport strike skill or mass executions that can refill AP.

Friendly Fire
Get an enemy to kill one of its allies
Done in two ways, either the dominate strategem or do crit strikes on characters that can be crazed (hellbrute, foetid bloat-drone, plague-bearer).

Opportunist
Kill 20 enemies with environment objects
Pillars or environment explosives count towards this achievement.

Corruption Cleanser
Destroy 50 Bloomspawn
You have to do Blooming missions, each has about 1-2 bloomspawns that you are required to slay. Get purging.

Surgical Excision
Collect a Seed using the Extractor Servo-Skull
You will unlock the Extractor Servo-Skull, use it on a seed bearer and this should pop.

Unstable Immaterium
Trigger 10 Warp Surge events in a single mission
Warp surges trigger once the warp levels hit 100%. For this one, you can end turns repeatedly to have these events pop up. If you do them in low corruption planets, you have to wait longer, but if you do them in high corruption planets, make sure your team can handle whatever comes your way.

Bloodless
Win a mission without taking damage
Bring units with high armor. Playing on lower difficulties also help.

Efficient Killer
Win a mission without using Ammo
Just use melee oriented characters. Doable with solo class achievements.

Just a Scratch
Win a mission using only knights with Light Wounds or worse
Only use knights that are injured in previous missions for a mission. They will have reduced max HP. Easily doable on easier difficulties and on seeding missions where only cultists are out there.

Phalanx
Win a mission using only Justicars
Firing Squad
Win a mission using only Purgators
Warp Flickers
Win a mission using only Interceptors
Field Apothecarion
Win a mission using only Apothecaries
Basically just do them with the indicated class. The field apothecarion one might be a bit harder due to apothecaries are essentially support class characters, but when in doubt, do it on an easy difficulty.

Brothers in Arms
Win a mission whith only 2 knights
Basically what it says on the tin. When in doubt, do it on an easier difficulty and use high level characters to do it on seeding missions.

Exercise in Restraint
Win a Spreading or Flowering mission without using Willpower
Spreading and flowering missions show up when the planet is highly infested. You can see what the mission is by checking planetary info Just go do those missions but without using the active skills that consume WP.

True Mastery
Have a knight learn all available class skills
Focus on getting the class skills instead of the upgrades.

Honoured Battle-Brother
Promote a knight to Rank 9
You need 1700 XP to get to the max rank. You have to grind for a bit.

Mind Like a Fortress
Acquire 20 Grimoires
You can get grims from armory rewards and several other ways. Get 20 of them and this should pop. You might want to prioritize on this one because grims will boost your research speed. Without grims, research will be painfully slow.

Nemesis Master
Acquire a Master Craft Level 3 Melee weapon
The Emperor Protects
Acquire a Master Craft Level 3 suit of Armour
Gunmaster
Acquire a Master Craft Level 3 Ranged weapon
During Grandmaster Reports, get your access level all the way up to 5 and they will show up in post battle loot. Just spend the required amount of requisition to grab them.

Tactical Flexibility
Unlock all Stratagems
Make sure to grab the grimoires and the library upgrades, otherwise the research will be very slow.

Patron of Deimos
Complete all Ship System upgrades
I suggest going for the augment chamber ASAP. The augment chamber will give you free servitors and improve ship upgrade speed.

Strike Force
Fill the Barracks with 20 knights
You can either get knights by directly recruiting them at the barracks for two requisition points a pop or you can get them at post mission rewards. You start with 6 and you need 20.

The Flesh is Weak
Acquire 5 Augmetics on a single knight
You have to unlock the augmentics chamber at ship upgrades. Augmetics can be used to help wounded knights.

Mass Extinction
Use Exterminatus 5 times in a Campaign
Exterminatus can be used to instantly kill all the infection (and innocent population) on a planet. You can use exterminatus once you arm the cyclonic torpedoes at ship upgrades. Do it five times.

Clean Slate
Achieve victory before any Bloom Flowerings occur
Basically prioritize on high corruption planets that are about to trigger flowering. Alternatively, I believe exterminatus also works.

Crisis Management
Achieve victory by Day 500
For this, you need to focus on getting grimoires and upgrading the library because you need that research speed to trigger many storyline missions. The finale also has a 45 day countdown so you need to keep that in mind as well. Grab seeds, but also make sure you don't use the seeds on unnecessary researches and upgrades because you need those seeds for the storyline and attuning. Might be easier on lower difficulties

Grand Master
Achieve victory in Grand Master mode
Basically just ironman mode.

Legend of Titan
Achieve victory on Legendary difficulty
Legendary difficulty can be pretty tough. Just beat it. Not much to this one.

Only in Death
Acquire the Venerable Dreadnought
Progress through the relevant story. You need to beat two missions to actually receive the Venerable Dreadnought.

For the Machine God
Purge all Archeotech Excavation Sites
Basically what it says on the tin. Do those missions.

Fleetmaster
Acquire the Pious Absolution
You need to beat a fairly long and hard mission to cleanse the Pious Absolution. You can then send some of your Grey Knights to auto-resolve missions.

Blood and Iron
Kill 50 enemies with the Dreadnought
You can bring the Dreadnought on Technophage missions, just keep doing those missions with your dreadnought. It shouldn't be too hard as the Venerable Dreadnought has pretty powerful weaponry.

Drone Army
Kill 50 enemies with Combat Servitors
You can unlock combat servitors for your techmarines. Bring them into battle. They aren't that powerful, so killing 50 enemies with them is going to take a while.

Dominus
Kill 10 enemies with Dominus Lunete
Similar to the Vakir 10 kill achievement, Lunete will take to the field with your knights. Like Vakir, she is not very powerful compared to your knights, so whittle the enemy down and let Lunete finish them off.

Arsenal of Destruction
Acquire all available weapons for the Dreadnought
Dreadnought weapons (and equipment) in general are unlocked in tiers and purchased with archeotech. Just keep grabbing the archeotech caches and buying equipment as they are unlocked.

Strategic Command
Win 10 deployments with the Pious Absolution
Send the Pious Absolution on missions that you can't reach or don't want to bother yourself with and wait for the auto-resolve. 10 times.

Master of the Forge
Win a mission using only Techmarines
Similar to the other classes' solo achievements. You can always bring servitors so they soak up damage for your techmarines.

Preservationist
Recover 5 Archeotech Caches in missions
You will definitely get this achievement before you get Arsenal of Destruction.

Execution Force
Acquire all Assassins at once
You first unlock an Assassin at around day 50. You get to pick a free assassin from one of the four temples. You can then spend 3 requisition to unlock each other assassin. Just buy the rest of the assassins and you will unlock this achievement.

Abomination
Promote a Culexus Assassin to Rank 9
Deadshot
Promote a Vindicare Assassin to Rank 9
Killing Rampage
Promote an Eversor Assassin to Rank 9
Reign of Confusion
Promote a Callidus Assassin to Rank 9
Keep using the Assassins until they hit rank 9.

Tactical Sabotage
Board and destroy a Death Guard Cruiser
You can now board the Death Guard ships and do a tactical mission on it as opposed to the previously where you can only do a choice. Board them and destroy them once you find a cruiser on the map.

Hive Exterminator
Destroy a Tentarus Hive
Complete the new mission type and you will get it.

Suffer Not the Mutant
Execute 10 Tainted Sons Enemies
Fairly self explanatory, you will run into these enemies later in the campaign.

Terminal Meltdown
Kill an enemy with Bio-Meltdown
You need to do this with the Eversor assassin. Make sure the Eversor "dies" near an enemy that has lowered health and the Bio-Meltdown will kill the enemy for you.