The outside of the ship is a pain, but there's no exploring needed.
There's nothing to find out there, so just head to the goal.
Pro tip: avoid as many aliens as possible. There's no need to try killing them all.
Head toward where you see the high tower on the map and jump up the platforms as high as you can.
Now run left and jump. This will bypass quite a few aliens. Now stick to the small upper platforms as much as possible while making your way to the goal. You'll end up having to kill 2 or 3 aliens, but you'll avoid most of them this way.
Hope this helps anyone that is having trouble with that part.