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.
Buy 20 unique Scavenger Market items in a single campaign.
Clear an entire encounter during the Breach turn.
Reach max rank with all Agents in a single campaign.
Relocate the same unit with Shelter and his ghost in one turn.
Win the campaign.
Complete the Sacred Coil Investigation.
Complete every Spec Op at least once in a single campaign.
Capture a Ronin.
Use every type of Breach point.
Complete a mission with only one Agent left standing.
Replace an Agent mid-mission with an Android.
Fully upgrade an Android.
Use Blueblood to hit 3 or more enemies with one Phase Lance shot.
As Godmother, activate Overtime and down an enemy on both turns.
Complete all of one Agent’s class training.
Use Claymore to detonate a Shrapnel Bomb with another explosive.
Complete 20 Assembly Projects in a single campaign.
Use every Agent in at least one mission.
Hack an enemy Android with Patchwork and trigger Self-Destruct.
Complete the Gray Phoenix Investigation.
Move a VIP with Shelter’s Relocate and Torque’s Tongue Pull.
Have Rank 3 Field Teams in all nine districts.
Capture a Praetorian.
Kill an enemy with Axiom while Berserk.
Have 8 Agents in the squad in a single campaign.
Use Verge to do 10 or more damage with one Mindflay.
Complete an objective with an action from Terminal’s Cooperation.
Use Torque to Tongue Pull an enemy into poison.
Equip an Epic Weapon.
Unlock all Field Abilities.
Launch a mission with no human agents in the squad.
Complete the Progeny Investigation.
Use Zephyr to hit 3 or more enemies with one use of Crowd Control.
Capture a Sorcerer.
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.