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