You can of course complete the dungeon without using any lockpicks, but Reed would have to swim around past every door and fight octopuses.
Sounds like the final boss battle is GLITCHED since there is that submerging sound every turn after the head went down the first time and I don't know why. And enemy balancing is so volatile, in order to make sure that certain battles aren't way too hard for some players you have to casualize everything down. I'm so done with this. I hate this game and I'm quitting game design.