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