Walk up to the ladder and press the Y button. Then move the left thumbstick up to climb and down to go down.
Press A repeatedly to climb faster and hold A to quickly slide down the ladder. Once at the top just use a Rocket Launcher. I won't spoil it by telling you why, you'll figure it out once you're there.
Alright, thanks a lot man. I pressed all the buttons to climb but I didn't use the thumbstick. Something so simple was stopping me from advancing in the game. <_<