A few factors that dance event photography

Gear
The better your camera, the faster you shoot to capture those moments.

Good Eye
For better composition(avoids loosing a limb from the shot) getting as tight as possible to reduce post-production.

Quick Reflexes
Especially important for group performances, different couples/dancers might perform different moves. This is tough as it is with only 1 dancer/couple.

Good understanding of the dance style
Knowing the dance style gives you a good comprehension of what to look out for, catching the great lines and this ties in to the musicality when the music hits a stop, generally the dancers will have accentuated movement or pose.

Great Musicality
Knowing the music allows you to foresee photo opportunities. Dancers often take advantage of musical flow, highs and lows of the piece to accompany their movements on the stage.

Great Positioning
This is probably one of the most essential of the lot. No amount of gear, quick reflexes, understanding of dance style or musicality will save you if you have a seat that is facing the dancers back. In most cases, it will be difficult to move during a performance so choose your seat wisely or you could well write off that shoot.