Star Wars: Battlefront II

Due to the close-quarters of the map, I would recommend playing as an engineer or heavy trooper for most of the map. The objectives are fairly straight-forward. If you haven't been using Darth Vader when he is available, I suggest that you do so. Be sure to kill Rebels as you go along to keep up your health. When you come to Princess Leia, be sure to choke her first, and then dash in and slice her up. If you're not playing as Vader at that point, go with a heavy trooper (or an engineer if you're good with detpacks). Lay down your mines throughout the escape pod bay, and she'll probably run into one sooner or later, even if she kills you first.

Just try to complete the objectives as fast as you can, and take every chance that you can to heal up.

Lil_literalist has the right idea. Personally, I always use a Stormtrooper and try to line up headshots... the extra grenades are nice. Play as Vader for as long as possible, he is your absolute best asset. Choking Leia may not be necessary unless she is moving around a lot. If you aren't Vader by the time Leia appears, you will absolutely need to be a Shock Trooper. Alternatively, if you have backup, play as a Scout Trooper while your friends soak up all of Leia's hits. Leia will always spawn in the same zone. This zone's easy to get to - it's across the hall from Command Post 1. Alternatively, to find it, you can go to where you began the mission (the invading lifeboat). Travel down the hall, hang a left, then turn left into the first door you find. Leia is in this room.

Good luck!