Here is the full list of all 19 BIOS achievements.
Kill 500 turrets or AI bots
Kill 500 Zombies
Get 10,000 Units
Kill 100 Zombies
Acquire at least one platinum medal
Kill 50 Zombies
Headshot 10 Zombies
Acquire at least one bronze medal
Acquire at least one silver medal
Acquire at least one gold medal
Kill 100 turrets or AI bots
Kill 50 turrets or AI bots
Destroy a missile fired from a turret
Kill either a turret or an AI bot with a grenade
Complete any race with 100% accuracy
Get 100,000 Units
Get 1,000,000 Units
Kill 1,000 turrets or AI bots
Kill 1,000 Zombies