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