When Dualcaster Mage enters the battlefield, it triggers, targeting Entering.
Holding priority, activate Goblin Bombardment by sacrificing Dualcaster Mage, dealing 1 damage to any target.
Resolve the Dualcaster Mage ability, creating a copy of Entering, targeting Dualcaster Mage.
Resolve the copy of Entering, returning Dualcaster Mage from your graveyard to the battlefield.
Repeat from step 3.
Optionally, you may cast both Breaking and Entering if you have an additional ({U} magic symbol) ({B} magic symbol) available to infinitely mill any number of players.