1). A tripod. This will help the background and anything static stay sharp. And it may help with something moving, as you are only dealing with the blur its movement is creating vs the blur of its movement + the blur of your camera movement not being locked down.
Try to take your photo as a moving target changes direction. As the fish (or whatever) turns around, it will be still for a split secind. You have a better chance at a sharp image when that happens.
Try to do a slower shutter speed and track with the fish. Keep the fish in frame and move the camera along with it as you take the picture. With luck you can get a sharp fish with a blurred background.
I don’t think they’d let me use a tripod, but tracking is a good idea… It certainly works for race cars. I’d probably be able to stop down too and rely less on perfect focus.
When you can’t use a tripod there are other better-than-nothing alternatives you can try for getting some equilibrium, like steadying the camera with your elbows against your abdomen, or pulling the camera forward against the neckstrap.