SF50 pilot reported an unstable landing resulted in a hard landing with landing gear damage.

Narrative

ZZZ is a public airport. It is surrounded by mountainous terrain. The airport sits in a valley. It has a 5;000 foot runway with one instrument approach procedure. The RNAV-A is a non-precision approach to an MDA of approximately 1600 ft. AGL over the airport. The final approach course is from the southeast and requires crossing over the runway to enter a right downwind for Runway XX. Runway XX requires right traffic so it actually fits into the traffic pattern. I flew the approach and when I had the field in sight I canceled IFR. I crossed over mid field as published and entered the right downwind for XX. The gear was down and the flaps were at 50%. Due to the rising terrain; I made the downwind turn too soon. I did not have the field in sight and began circling to the base. I saw the threshold and realized I was still high. I deployed the flaps to 100%. I was too fast and landed but bounced up due to excess speed. The end of the runway was approaching and I forced the airplane down again. This time it hit too hard and collapsed the nose gear as well as flatten the left main gear tire.Throughout my flight instructing career I salvage bad approaches on a regular basis with students. That cannot be done in a turbine powered airplane like the SF50. I should have executed a go around as soon as I rolled onto final and realized I was too high. It would have required a right hand pattern again but I could have stay above the mountains until it was time to descend on the downwind.