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