Chemical peelings do work very well but need caution and a bit of expertise.
TCA 30-50% applied to the spots will erase them immediately but adverse reactions might happen, full face TCA peeling at 25-35% is effective but might not erase all spots (some seem harder than others to wipe out).
TCA at those concentrations might leave scares, especially if no chemical peel has ever been performed before, glycolic acid peelings are not very effective by themselves (at least in the immediate) but do "condition" the skin to better cope with subsequent stronger acids, more than 35% is worthless in my experience, it only causes more irritation without being more effective.
A safer compound is glycolic acid 20-25% mix with cogic acid 1-2% to be used just on the spots, it is quite aggressive but more predictable and "easier" than TCA, same efficacy in my experience and definitely preferable.
For whole face treatments with glycolic-cogic acid I would suggest caution, spot test before and a smart idea would be to play it safe first (10%+1%), I never did that yet.
Malic acid < 10% + cogic 1-2% should work well, glycolic+malic+cogic should as well, personally never tried those mix yet.
Any of the above in a hyaluronic gel base would be easier to apply (doesn't run) and attenuate some of the irritation, I did only 1.5% hyaluronic acid gel + glycolic 10-15% full face everyday, nice and good peelings, not effective for "harder to erase" spots in the short term (30 days or so) but nice for general better looking skin, I prefer it by far to once a week 35% glycolic only, it doesn't need buffering afterward.
I am using 1.5 % hyaluronic acid gel + 4% niacinamide right now but is too early to report definitive results, so far I like it.
Dermarolling might work up to a certain degree but is much slower.
The glycolic + cogic gives immediate results if you don't mind some scabs for a few days.