Adverbs for Dirty (Dirtily?)
Solution 1:
Dirtily is the adverb while dirty is used as an adjective or verb. However, to talk dirty is an informal phrase and is always used this way.
talk dirty
informal talk about sex in a coarse or salacious way.
I assume that you wouldn't want to talk about talking dirty in a formal context anyway, so talk dirty should be fine.
Solution 2:
Dirtily is correct, but it does sound a bit clunky. A few alternative adverbs: foully, uncleanly, shamefully, basely, vulgarly, coarsely.