There are two locations where you can swim underwater in this map. For both you will need to grap the artifact at the far end of the ship first (it cant be missed).
Your first underwater location is right under the artifact. It is the engine room.
The other location is under the starting area at the very front of the ship. It is called the Cargo Room.Both areas are locked behind pretty expensive doors (around 1750 points on solo). Naturally you should not drain the water.
I would recomment going to the Cargo room. You can swim around with plenty of space and can pretty much go up anywhere for air.
The rest should be self explanatory. Grab a good gun, swim underwater and kill every zombie you see. It should only take about two or three rounds.
You can do this on casual difficulty. I would recommend not taking any bots for this as they tend to steal kills.