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