This is a known problem with the TG's and moving objects, especially when trying to use a strobe. The camera tries to expose for the ambient light, so the shutter speed will nearly always be slow underwater except near the surface at midday in tropical water.
Tricks people try:
** Use EV compensation of up to 2 stops, that is, force the picture to be dark, then have the flash do the illumination.
** Use A mode and force the aperture wide open.'
** Higher ISO.
** Some combination of all the above. Time to play...
** Sports Mode. here is what one fellow said on another forum:
Sports mode will attempt to use 1/500 or faster depending on available light. As light drops, I believe it will increase ISO up a max of 1600. But, if it can't maintain 1/500, it will naturally start using lower shutter speeds. Flash may help freeze motion due to its short output duration. Yet, the shutter speed will still be slow and the flash has limited range.
If you have pushed the ISO up to 1600 and don't have a fast enough shutter speed, you don't have enough light for this camera to produce what I'd consider a clean image. The best you can do to avoid zooming and take advantage of the relatively fast f/2 lens.