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Alchemist bombs are fire based and fire doesn't work underwater. In addition to that, thrown weapons don't work under water. The solution for a bomber alchemist is Explosive Missile discovery + any non-fire bomb discovery + underwater heavy crossbow (I say heavy because the ROF is exactly the same as a light crossbow when using Explosive Missile).
Once you get those you will rock underwater combat. Before you get those you will totally suck.