For Jhen Mohran, priority 1 while it is moving, is to not let it hit your ship. So make sure you have a pickaxe and the ballista binder.
When the quest starts, pick up as much as you can from the ships cargo, with the exception of the Ballistas, then go upstairs, and pickup ballistas (You will get about 6 or 7 before Jhen does his first rock attack), Then go to the Ballista shooter and shoot its tusks as best you can. Ballista damage ignores armor, so you don't have to aim for weak spots, however, broken tusks give more rewards.
Eventually it will get close, switch to Ballista binder and bind it when it gets ready to hit the ship. Once it gets loose, it will try another hit, at that point, use the Gong. Once it recovers, it will move close to the ship to give you a chance to get on top of it. Harvest the spots on its back at this point (it has 4 mining spots), and then go to one of the 2 weak spots on its back ridge. (You will notice these have a crack on them). When you see the Jhen Mohran shake a bit, it is getting ready to throw you off. Jump off or take heavy damage.
At this point when back in the cabin, pick up the Ballistas from the ships box and go back upstairs. Jhen will jump across the ship, and this time it will try to ram the ship head first. Again, use the Binder, and on its second charge use the Gong, and then climb on it again, putting the Dragon Bombs on its tusks and going back to the weak spots, remembering to jump off when it shakes.
Jhen eventually will go far away from the ship getting ready for its direct ram. You will notice it will go underground, jump up once, and when it is out of the ground the second time, hit the Dragonater, which after charging up for a little, will do a direct heavy damage to Jhen. Then the cycle repeats itself, with the Jhen starting up from the right hand side.
When you have done enough damage, it will take you to the final showdown. At this point, shoot off your remaining ballista shots at its face/tusks and some cannon shots when it gets a little closer. As soon as it gets close enough, use the dragonator on it. (As soon as you hit Jhen with the dragonator in the final showdown, the quest is won, as long as your ship doesn't get destroyed. It is a matter of using your binder, gong, and flinching it properly). Since the dragonator has a 10 minute refresh, you could possible do it twice. Put the Large Barrel Bombs on your ships edge, and when Jhen gets close, blow them up to cause him to flinch and back off, if your binder or gong are not ready yet. Whenever possible, continually shot at Jhen's fins. When they are damaged enough, he will flinch, and back up a bit.
You can either win by time out, or outright kill the Jhen if you are doing enough damage. Jhen's weakest spot is the inside of his mouth, however, this is a hard spot to shoot at full strength (Proper distance is 2-4 regular rolls away from target), so it is best to aim for it's Fins, for quicker flinches and wounded fins also give you more rewards at the end of the hunt.
I am sure you have already been using most if not all of the suggestions I have put, but it never hurts to get a reminder.
One more thing: Pierce shots will not grant you the most damage vs Jhen, since only the first part of pierce will do damage on its weak spots, and the rest will just go through his non-weak spots, or just air, in the case of it's back-ridge. You will notice much better damage by using Normal 3 shots and scatter shots. If you have Ice Elemental shots, that is his biggest weakness, and try aiming these tasty shots inside his mouth, if you are guaranteed to make em go in there, or just focus on his weak points. Also, evade extender is not needed on such a slow moving beast. and if you take up my suggestion and will not use Pierce shot (I know this sounds hard to do since you have it as crouching fire, but trust me on this), try to go for Recoil down, reload up, Load up and/or Cluster shot+. (A few cluster shots in the mouth of Jhen can quickly give you a flinch when you most desperately need it.)
Overall, this fight is mostly about avoiding him attacking the ship. Killing him is a bonus prize for properly preventing him from attacking, and you doing damage while it is positioning himself to try and attack again.
Hope this helps, and happy hunting!