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