Here is the full list of all 16 Zero Hour achievements.
Place and Utilize Spy Cam
Get your first grenade kill
Get a C4 kill
Get a good Training Ground Time
Get a kill with a door trap
Pick up the attacker’s gun
Defuse a bomb
Survive a 1v1 situation
Kill all of the enemy team single-handedly
Extract hostage
Reach Top Tier
Reach Tier 4
Reach Tier 6
Reach Tier 9
Reach Tier 2
You have gone through the training ground tutorial