This trophy can be very buggy and won't pop sometimes. If you have gotten the most kills in a match and still not unlocked the trophy try selecting a blast match by map and try to get into a less then full match, the fewer the better. Try and have the most kills at the end but instead of ending at max kills have the match time out.
Credit goes to ShaDoW-SlaYa:
http://www.gamefaqs.com/boards/720952-star-wars-battlefront/...I did the method he mentioned, I'm not sure if it will work with private matches
Edit: trophy has been patched thank you to Amphiprion11513 for confirmation!