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