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