This is the trickiest trophy in the game. The first 4 Zones have a blue 'Landing Pad' looking area somewhere in the stage (very obvious placement, not hidden). Standing in the middle of the pad will take you into a Bonus Area of sorts. You have no vehicle, which makes it much easier to die. If you die you are spawned back outside and cannot complete the base. Oh, and you must beat all 4 Bonus Stages in one playthrough. SO BE CAREFUL!! It's not as difficult as it sounds if you know what to watch out for.
Kamikaze Troopers are your biggest threat. They are the soldiers in red and they explode when they die. DON'T LET THEM GET CLOSE TO YOU!
The other hazard to avoid is destroying barrels when you're near them. The subsequent explosion will kill you as well as your enemies.
Above all, TAKE YOUR TIME. You'll spawn enemies quicker if you try and move fast through the area. Your health recharges, so take a breather.
Follow those tips and the bunkers will pose almost no threat for you. When you reach the 1UP at the end you'll be transported back outside to continue the game.
NOTE: The trophy will NOT pop after you finish Bunker 4 but rather, after you finish Zone 4.