How can an aquatic salamander survive with out hind limbs and very tiny forelimbs?

Typically, aquatic salamanders still have a very strong body and flat tail which it can use to propel itself through the water. If the animal you are referring to is an axolotl, it only needs to move through the water in order to filter the oxygen from it with its gills and to acquire food. They can swim very much like a fish when they have to move quickly.

If you simply have an animal that only has front legs, but still has gills protruding from its head, then it is a very young salamander and all of the limbs will develop in time.