My wife is a Filipino-Chinese and has a fair complexion but she has
trouble with the darkening of her underarm. She has applied several
types of cream to whiten it and even went for skin feeling but there
is no changes or improvement to whiten the complexion of her underarm.
Is there any possible solution to whiten her underarm by using any
natural products or medicated creams for topical application?

Use of such cosmetic bleaching creams can actually be dangerous and
harmful for your wife. It has apparently become a lucrative industry
for international cosmetic companies, and in my opinion, sends a
negative message to women of color.  Unless there is some underlying
pathology for the darkened appearance she should leave well enough
alone. If there is some concern that there is a pathology, she should
consult a reputable dermatologist or endocrinologist (M.D.'s).

She should definitely see a dermatologist before doing anything else.
The condition MAY be simply a case of more pigmentation than is normal
or MAY point to an underlying problem (e.g. 'acanthosis nigricans'). A
qualified dermatologist needs to take a look.

James