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