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