The main objective of an Assassin mission is to destroy a targeted Nomad in any way, usually by luring the ship into danger (such as a system with life planets).
Mission Briefing: Edit
I need you to do a bit of dirty work for me. Some rogue ships need to be brought down. Here's the first one.
Mission Success: Edit
Good, good. I'll be in touch.
Mission Failure: Edit
Don't worry, I won't punish you for that. Just get back in there and finish the job. You may not be able to kill it directly.