From a technical standpoint, I can see this requiring some fascinating processes.
First, of course, is reducing the body's overall fat-content; 'reducing', rather than 'eliminating'. (Them ta-tas ain't made o' muscle, after all.) Human bodies do need a certain amount of fat to be healthy, females moreso than males but only by a relatively small amount.
Second is shrinking the skin, with a bonus detail of eliminating the stretch-marks produced by the initial weight-gain.
Next up would likely be a lot of 'internal repairs' to every organ, as well as the connective and cushioning tissues.
How? "Magic", of course, but what would that mean?
Personally, I can easily imagine the excess fat (and possibly the excess skin, as well) getting converted into a LOT of energy, which could then be used to fuel the rest of the process.
The tricky part would probably come from extremely precise control of neural-signals, because the patient is clearly not only quite conscious (note how her eyes observe the changes) but displays not a jot of discomfort. No heat-stress from converting all that tissue into energy (she doesn't show a DROP of sweat), for example.
Overall, though, a wonderful sequence showing excellent 'motion-control' and contouring, particularly when the former is 'visibly changing' the latter from one panel to the next. Thank you very much for sharing this!
The 'zap' probably contains a LOT of different effects wrapped up in what the human eye can only perceive as a single bolt of energy. Pain-management, manipulating all kinds of tissue beyond just the 'excess fat', shrinking her epidermis to keep up with the changes going on underneath, and so on...