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