It does stay in the water most of the time. It is possible to shoot it with explosive shots, when it pops it's head out of the water to shoot it's water jet at you. The explosives, if you hit it, have the same effect as sonic bomb, so not only are you hurting it, you have the possiblilty of getting it out of the water.
The plesioth will, sometimes, come out the water, but it usually takes alot of persuasion.
You can take with you a lot of explsive shots if you take with you sml bone husk and wyvern claw. Combine them to make clust lvl 2. You can have about fity of those shots, so it is usually enough to damage it enough to get it out of the water. On the rare occasions that it does come out of the water, shoot it with thunder and piercing shots.
Of course still throw sonic bombs at it, just to give it that litte extra encouragement to get it's butts out of the water.