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