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