So all you need to do is eat 50 flies over your time playing Battletoads. After finishing the game and completing everything else I had about 25 flies eaten.
The quickest way to grab this is to save just before the 4 flies appear in the first level. So after you have defeated the two red flying dragons, jump over the gap and kill the red devil things (might be silver) then save. Eat the as many flies and you can and then re-load your save.
You do not need to exit to the main menu for the flies to count. I have only done that in the below video to show you the percentage Increases. The achievement won't unlock until you quit out to the main menu.
UPDATE: As per the first comment, you can apparently have the achievement unlock in game without quitting to the main menu.