by maxing his beauty (the contest stat >.>;; just keep feeding it pokeblocks that raise it's beuty then, once it won't eat any-more, level it up. if it doesn't evolve, then you need to breed a new one and try again)
use specific berries to create pokeblocks that up beauty condition, feed them to feebas, max out beauty condition, and level up. I am not sure what berries are the best. The main site has a section on berries.
there is a guide on the serebii homepage about how to get the highest level beauty berries...go read it make the berries and feed them to the feebas until the octagon of stats is full on beauty