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