One wonders if these leviathans are just very cranky herbivores, or if they're preying on smaller, more abundant animals that might be more easily caught.
If you're determined to face such monsters, harpoons may work. Simple harpoons would be very risky, since they don't so much inflict mortal injury as let the hunters latch on long enough to tire the animal out. Basically being strung onto a very large, very powerful, and very unhappy creature is going to be dangerous no matter what kind of vessel you're in.
There is such a thing as explosive harpoons, which could do more damage. But even with our small earthly whales there's historically been some trouble with the dead animal sinking before it can be retrieved.
If you want to use an up-close attack, it will probably be best to go after young leviathans in some way, like orcas hunting a humpback. Depending on the species' reproductive cycle, this might also be a slightly more sustainable option, since there would still be adults left to reproduce. The only issue here would be that this would make Mama very unhappy, assuming she sticks around to raise the baby. The hunters would have to separate the baby from the mother.
Another thought: is the planet entirely water? If there are some landmasses, and if your leviathans use a whale-like sonar, or an eel-like magnetic compass, the hunters could conceivably create a device that could confuse the animal's navigational ability and drive it towards land, beaching it. When whales are beached naturally on earth, they become massive, readily available sources of meat for all kinds of animals. And there's some evidence that manmade technology may contribute to whales beaching. With your leviathans, this kind of hunting would let the humans hunt from a distance, conserving their resources, minimizing the risk to themselves, without damaging the animal or risking the loss of any part of it. If there are no natural landmasses, perhaps the hunters could construct some other large, reusable trap to drive the leviathans onto/into.
Ultimately, the best option will the one with the least risk to the hunters, the least amount of resources lost in the process, and the least amount of damage done to the animal being hunted.