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