Easiest way--which works almost every time on hard--is to jump back down once you have 'activated' the chopper and go back all the way to the platform running around the outside of the ship. With full armor, health and ammo, you will be able to take out the chopper by crouching behind the platform wall and popping up to shoot the gunner.
For the rest of it, first make sure you took out the [2 I think] guys on the upper deck who you can see from the lower deck. Back on top, climb the ladder and run left, then drop prone and focus on taking out the 2-3 guys facing you--ie in the stern of the boat. Life gets a lot easier when your attackers are all coming from one direction, the prow of the ship.
Take cover in a place which will mean most guys approaching will be literally foreshadowed by their shadows! If you get badly beat up, you can always jump back in the hole and roust up some health/armor from the lower regions.
There is also what I regard as almost a cheat, you can climb out of the hole and run straight to jump into the water. Then swim back and shoot the boats chains, and level finished. I don't do this, so I don't know offhand if you need to take down the chopper first.