I'm not familiar with that specific camera, but in general, flash sync speeds are limited by the camera's shutter. Fixed-lens cameras typically have lens-plane, or 'leaf' shutters - typically a number of blades that open and close very quickly, exposing the entire frame of film (or, in modern days, sensor) to the light at once. This allows very fast flash sync speeds, often up to 1/4000s.
On the other hand, most interchangeable-lens cameras, with few exceptions, use a focal-plane or 'curtain' shutter. In a basic setup, you have two light-tight curtains - one covers the frame, the other sits off to one side. (or above/below, depending on implementation). When you take a picture, the first curtain moves away from the second, starting the exposure. After the exposure period is complete, the second curtain slides in, blocking the light and ending the exposure. If you have a flash attached, it needs to fire in the period after the first curtain is done sliding away, and before the second curtain starts moving in, as its pulse is extremely short, and needs to hit the entire frame.
However, the curtains can move only so fast - for short exposures, the cameras don't wait for the first curtain to slide all the way away before they start moving in the second curtain. This results in a strip of light moving across your sensor, limiting the time that it is exposed - but it also breaks flash sync, as it doesn't leave any single point in time when the entire sensor is exposed and the flash can fire. If you do fire a flash while your sensor is only partially open, then only a part of your image will get exposed, ruining the shot. In your camera, the fastest the shutter can operate with flash sync is 1/160s which is pretty typical; other cameras may reach 1/250s and rarely 1/320s or 1/500s.
There is a way to partially mitigate this issue called High-Speed Sync - in this mode, the flash fires a rapid (I believe it's typically 40kHz) series of flickers instead of a single pulse, which serve to expose the image as that thin opening races across the sensor - but it greatly reduces effective flash power, and to the best of my knowledge, no underwater flash supports it.
Most advice that I've read is to not worry overmuch about it and set the camera and flash to use ambient light to expose the background and strobe light to expose the primary subject. In more direct terms, you close the aperture to a value far smaller than required to expose your shot in natural light (f/8, f/11, or even f/16) at your sync speed (1/160s), and ISO to the lowest value supported by your camera (typically 100), then use your strobe(s) to actually light the subject. This way, even if your subject is moving, very little of the natural light they reflect during the 1/160s that your shutter is open actually reaches your sensor and the picture is actually taken with the extremely short pulse emitted by your strobes, without which, the photo would come out almost completely black.
