As SeeYaLater! clarified above, no, no mythical Pokemon are needed to complete the Pokedex, since not everyone has access to events that distribute them.
These Pokemon are:
Mew, Celebi, Jirachi, Deoxys, Manaphy, Phione, Darkrai, Shaymin, Arceus, Victini, Keldeo, Meloetta, Genesect, Diancie, Hoopa, Volcanion, Magearna, Marshadow, Zeraora, and Meltan/Melmetal.