Go to the Backyard Battleground
Go to the Quest Board
Epic Quests can be identified by the yellow exclamation mark on them.
Quests only update once every two days, and in two sets of quests I've only seen one epic quest so this will take a while to do.
My first and so far only epic quest involved winning 15 gnome matches under multi-player quests, I did this in private matches, with no zombies under team setup and always picked a plant when spawning in.
As there were no zombies to stop us, winning was a breeze