Chemical Peel on Butt, Waist and Leg?

Doing several medium TCA peels such as a 20-30% TCA peel every month for 4-5 sessions do nice to lighten up dark areas, especially if sunscreen and bleaching creams also are used as well.

You could, but you could also risk further injuring the skin with a chemical peel in areas that are already hyperpigmented. 
Injury to the skin, especially Asian, Brown, East Indian or Black, is prone to hyperpigmenttion after injury, bites, surgery, sclerotherapy ...
Sometimes, it takes up to 3 cycles of skin growth, 180 days each, for the hyperpigmentation to fade, if at all, without adjunctive therapy:
There are some topical creams that we use for patients with hyperpigmentation from a myriad of causes in the legs: from venous insufficiency, following wounding, following surgery, following sclerotherapy ...
We recommend Sclerovase and Scleroquin plus topical creams.
You can add retinoid RR Complex Retinoid Repair Cream as well. 
Scler-x post inflammatory hyperigmentation relief complex is a great supplement to take as well. See link below. 

Chemical peels can be risky in areas other than the face.  Healing is much different in those areas.  There are some pigment lightening medications so you might check with a dermatologist.