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