Here is the full list of all 40 XCOM: Chimera Squad achievements. It takes around 60-80 hours to unlock all of the achievements on Windows.
Complete all versions of each Faction’s Takedown mission over multiple campaigns.
Use Zephyr to hit 3 or more enemies with one use of Crowd Control.
Win the campaign on Impossible difficulty.
Use Blueblood to hit 3 or more enemies with one Phase Lance shot.
Hack an enemy Android with Patchwork and trigger Self-Destruct.
Clear an entire encounter during the Breach turn.
Complete an encounter by only dealing damage with melee attacks.
Use every Agent in at least one mission.
Win the campaign.
Complete the Sacred Coil Investigation.
Buy 20 unique Scavenger Market items in a single campaign.
Relocate the same unit with Shelter and his ghost in one turn.
Reach max rank with all Agents in a single campaign.
Capture a Ronin.
Replace an Agent mid-mission with an Android.
Launch a mission with no human agents in the squad.
As Godmother, activate Overtime and down an enemy on both turns.
Complete the Gray Phoenix Investigation.
Move a VIP with Shelter’s Relocate and Torque’s Tongue Pull.
Complete all of one Agent’s class training.
Have Rank 3 Field Teams in all nine districts.
Complete every Spec Op at least once in a single campaign.
Use Claymore to detonate a Shrapnel Bomb with another explosive.
Complete 20 Assembly Projects in a single campaign.
Use every type of Breach point.
Use Torque to Tongue Pull an enemy into poison.
Fully upgrade an Android.
Capture a Praetorian.
Have 8 Agents in the squad in a single campaign.
Equip an Epic Weapon.
Unlock all Field Abilities.
Complete the Progeny Investigation.
Use Verge to do 10 or more damage with one Mindflay.
Complete an objective with an action from Terminal’s Cooperation.
Complete a mission with only one Agent left standing.
Have Kinetic Armor on all 4 squad members at once.
Capture a Sorcerer.
Complete a mission without killing a single enemy.
Kill an enemy with Axiom while Berserk.
Complete the tutorial.