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