How I do it-
Check fitting for any filler, mastic or painting that has sealed it on. Remove any seal with a stanley knife or sharp blade.
Wiggle the fitting a bit to make sure it's unstuck. Then get a strong flat wide blade such as a filling knife, a metal ruler or such (I've done it with tea spoons before). Use that to wedge between the plaster board and the inside of the fitting lip. Fulcrum action.
You should now have the fitting slightly away from the ceiling, maybe 10mm on one side, now do the same action 180 deg away making sure that as you pull that side of the fitting down the other side doesn't just fall back in towards the ceiling (the natural action of the retaining springs tends to make the fitting want to do this).
Now you should have a big enough gap all round the fitting to get your fingers on the damn thing.
In a gentle, firm motion pull one side 10mm, then the other side 10mm, at this point the springs should be offering less resistance (because they have been force towards the sides of the fitting /towards vertical) and you either repeat the pull on one side then the other, or pull the whole thing downward and out.
If you damage the plasterboard doing so (often the springs cut into plasterboard), make a hardboard polo mint with the inner hole to match the fitting spec. Cut in half, butter with no nails and place in position inside the ceiling.
Once set, fill to surface, once dry sand down and shape to the polo mint template. The template will provide a element of firmness that filler can't and allow the replacement and occasional removal of the fitting without damaging the ceiling in future.
Hope that makes sense, and if you are on heavy meds please don't use ladders or go near power on the meds. Hope you get better, or at least have good days.