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