!CruisinForABruisin - Complete mission with all cruiser structures intact. - 2000 Plex.
Peanut Butter Relapse - Deal 8,000 damage. - 1500 Plex.
Nero the Hero - Complete mission using only Auxiliary Bay deployables. - 2000 Plex.
The Auxiliary Bays are in the upper left part of your hanger. Click on one to bring up a list of Archetypes. From there you can pick a specific ship. Choosing [Active] will place that ship with your current loadout for it into the bay. You can also pick any templates you have saved or use a Prebuilt ship.
Auxiliary Bay ships will show up as green dots on the map.
For Nero the Hero, just never fire your weapons. It's unlikely you'll get both Nero the Hero and !CruisinForABruisin in one mission unless you're on a low difficulty level or you're very good at tuning ships for Auxiliary Bay use.