You could try a few things. Sam's tours are well known, as are fish'n fins.
Other option is liveaboard, I think there is a Palau aggressor and also Ocean Hunter.
As for marine life, Palau is supposed to be world class with one particular spot (blue corner) frequently referred to as the worlds best dive site. Lots of big things, especially sharks.
I doubt it will be cheap though and could be pretty scary, reef hooks and hanging on are the order of the day.
As for getting there, Manila then Continental airlines to Palau.