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