i know this thread is a week old, but nobody really addressed proper bracing in these responses. JFG touched on it with his references to core, but it's not so much core weakness from what I can see as it is not bracing your core before each rep. I can tell you're not doing it because as soon as your feet get set, you're beginning your descent.
I would really recommend reading up on bracing and watching some videos on it, because it's hard to explain in a single thread post, but you're basically trying to fill your belly (not your chest) with air. You inhale strongly, expand your abdomen, and hold it that way throughout each rep. You'd be well served to 'reset' your breath before each rep while learning the technique. This will help you tremendously. The way I like to teach it, to get some tactile feedback while learning, is to put on a weightlifting belt, and try the breathing technique. You set the belt to where you can feel it all around your abdomen but it's not super tight. Then you try to fill the belt with a big inhalation. You press out in all directions against the belt basically. You would just do this standing up, no bar or anything on your back. From there you would practice some air squats with your breath held and core braced. Then you'd move on to performing the movement with a bar.
Hope this helps, if my explanation is not clear, please ask questions.