(BigBoss Mode) - Defeat Pilot. Unlocks F-15J Eagle "305th Squadron"
It's not too complicated (but does require a lot of time).
First, unlock the first five Premium Rewards, by shooting down the specific wingman Big Bosses, as explained in G03, then challenging each one in Big Boss Mode.
Next, you need to obtain Best Guy or Predator rank, by playing online in Multiplayer. This rank can't be obtained offline in Challenge Arena. Once you have reached Best Guy (or Predator), hop into Challenge Arena, and shoot down a plane, then land and exit. Select your Big Boss menu, and F-15J 305th should be available to challenge!