I concur with Enguroo's answer, and their suggestion to omit the noun "groups" but if push comes to shove, and you don't want to leave out the countable noun, choose b.)
b.) 80% of what I listen to are K-pop groups.
The percentage refers to numerable units, with a little rewording we see why the verb must be plural
80% of the groups I listen to are K-pop
However, it's a bit awkward to start a sentence with a number, a fraction or a percentage. @Edwin's solution is preferable,(“… I listen to K-pop groups 80% of the time”) otherwise leave out the percentage and be less specific, e.g.
Nearly everything I listen to is K-pop music.