Pick a solo Team Deathmatch game, then select any map you wish and create a lone bot. When selecting your class, select 'Flag Ship' and then repetaedly kill the bot (and the escape pod if you can). After about 22 kills you should have around 250,000, unlocking the NCC-1701 trophy.
When Death Match mode startss, pause the game and press R2, L2, R1, L1, TRIANGLE, SQUARE. Your ship's rate of fire and regeneration rate will increase until your ship is destroyed. Enabling this code unlock the "Kobayashi Maru" trophy.