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