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