Qualifications
This isn't the toughest gig to land. The first and most important requirement (and the one that shrinks your competition considerably) is that you have to want the job. That said, even though you don't need a college degree to work as a dredge operator, dredge captains aren't going to hire you based on your proficiency with an erector set.
The other basic requirement is you have to have the physical ability to do the job. Work as a dredger requires someone who can move heavy objects around, operate machinery, handle tools, assemble pipes and other equipment, and be able to tolerate super-long shifts full of hard work. Does that still sound like you?
Beyond wanting the job and being strong, having experience with construction work would certainly be helpful. Not only can you show the hiring manager that you know how to work on a team, you can assure them that you are adept at physical labor.
Bonus points if you operated a bulldozer or crane—just don't tell the interviewer that you snuck into the bulldozer when no one was looking and flattened a few walls (which is why you're looking for work now).
Finally, you can increase your chances of getting hired by showing up for the interview wearing a hard hat. No, just kidding. Well, go ahead and try it, and let us know how it turns out.