I'll forewarn you. What you are about to see is real. Somewhere, a "trainer" really thinks this is a good idea to perform. View at your own risk.
Are you ok? I hope no one was eating while they watched that. If you were, I apologize; take a minute to clean up your keyboard.
Better? I'm not. What an awful awful decision to have a client perform this exercise. Not only that, but they called it a 360 squat. Last time I checked, 360 degrees was a full rotation. If you only jump and land halfway, then its a 180. How's your geometry, brah?
I was hoping that everyone was now up to speed about unstable surface training, but if you aren't, here's the deal.
Doing an exercise (squat) on an unstable surface (Bosu Ball, Airex pad, Versa Disc, etc) doesn't serve to do anything except make you weaker and slower. The idea behind strength training is stronger and faster. If you are able to squat 315 normally, and then get on a Bosu Ball and squat 135, what function does this serve? You're using a submaximal amount of weight and decreasing the amount of force you are able to produce. Cool. Where do I sign up?
So, Bosu 180 Jumps? You cant use any weight. Sucks. You produce less force, resulting in a submax height jump. Shitty. Increased chance of slipping/falling on the ball and hurting yourself? Check. Shitty.
Now, there are much better ways to perform similar exercises. Take out the Bosu Ball, perform the exercise with appropriate intensity and you have something worthwhile. Frankly, any plyometric exercise sans unstable surface is going to be a really good idea.
Keep it simple. Pick up something heavy.