Mirror-Mad Phantasm does not have summoning sickness.
You have a way to draw a card.
You have at least two opponents.
({1} magic symbol) ({U} magic symbol) available.
Steps
Declare Mirror-Mad Phantasm as an attacker.
Mirror-Mad Phantasm's myriad ability triggers, creating a token copy of itself tapped and attacking each other opponent.
Activate a Mirror-Mad Phantasm token by paying ({1} magic symbol) ({U} magic symbol) , causing you to shuffle it into your library, then reveal and mill your entire library due to not having a card named Mirror-Mad Phantasm in it.
Draw a card, causing you to win the game due to drawing from an empty library.