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