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