As has been previously mentioned, in the base game, defeating Mega Satan with any character is only necessary for an ending, which is necessary for the Platinum God achievements.
However, with the Afterbirth DLC, there is now an unlock/achievement and a completion mark for each character that is earned by defeating Mega Satan. Defeating him prior to purchasing the DLC does not count for these, unfortunately, presumably because the game did not track who had defeated him.
Furthermore, there is another set of unlocks/achievements for getting all Red completion marks (Hard/Greed modes) with each character (Mom's Heart, Satan, Boss Rush, Isaac, The Lamb, ???, Ultra Greed, Hush, and Mega Satan).
All the unlocks related to defeating Mega Satan and getting all the Red completion marks are babies for second player to use in cooperative mode.