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