seek strong, hard to break plastic material

Note that boots are often used in snow and slush, so you need a plastic that won't become too brittle at low temperature -- it should have a glass transition temperature significantly lower than the lowest temperature the boots would be used at.
Plastic isn't the best choice for this. All of the ones I've seen are metal. If you want it to look like plastic, you can powder coat a metal core, or injection mold around a metal core.
You don't say why you want to use plastic here. If you're planning to injection mold it, you can't use most thermoset plastics. (Integrated circuits are molded in thermoset plastics, but those are very special formulations.)
The strength of the plastic will be highly dependent on the filler. You might want a chopped glass fiber filler for good reinforcement. The filler may need to be treated with a silane coupling agent or some other modifier to promote adhesion between the filler and the matrix. The epoxy-fiberglass used in printed circuit boards usually has a characteristic green color because of the copper used to promote adhesion.
A problem with any non-spherical filler is it will entrain to the direction of flow during injection molding. Clever design of the mold can take advantage of this to increase strength in the desired direction. In a buckle, you'd want the fibers to be aligned along the length of the spokes, but you may create a weak spot where the streams flow together. There won't be any fibers bridging this spot, so that's where it's going to crack, unless you do something about that.

We have used metal buckles, which caused problems in washing and drying.

What were the problems?

could try delrin.
Also, use the plastic selection tools at

metal overheat in dryer, electro-plating dis-colored in wash.

Was this a microwave dryer? If not, why would plastic not do the same thing?
If you used the metal part as a core for powder coating or injection molding, you would not electroplate it. You might pickle it shortly before coating or molding to improve adhesion. After coating or molding, it would be sealed againt the environment and not discolor or rust.