Breathing squats earned their name because of the oxygen debt and heavy breathing you experience as the set progresses.
I first discovered breathing squats when I did a "workout swap" with a powerlifter friend of mine. I gave him Danish Intervals to do on his assault bike and he gave me this breathing squats workout. Neither of us were each other's favourite people afterwards.
On the surface, it's a simple workout and you wouldn't expect it to be all that hard, but done right the breathing squats workout is very tiring. Don't underestimate the neural fatigue you will experience. You will need more recovery time afterwards than you might expect.
Warning: If you're going to do these, please do them in a squat rack or rig up some way to catch the bar if you fail (and if it's a bit Heath Robinson, test it with lower weights to make sure it works).
These will hurt and you'll almost certainly have DOMS for a few days afterwards. But if you have limited time available for training, breathing squats could be the way to go.
How to do it...
Do a thorough dynamic mobility warm up for at least 10 minutes, followed by 2 or 3 light sets to groove the movement.
Load a barbell with a weight that you could squat for 10 reps.
Walk the bar back from the rack and squat 20 repetitions before replacing the bar on the rack. If you need to rest, simply stand there and breathe with the bar on your shoulders - the set takes as long as it takes to get the twenty reps done.
Replace the bar on the rack, take a good rest and perform at most 2 assistance lifts before calling it a day.
Cool down, including any mobility exercises you need.
Eat and rest!