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