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