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