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