If the target creature is an illegal target when Brash Taunter's last ability tries to resolve, the ability doesn't resolve. If Brash Taunter is no longer on the battlefield, the target creature won't deal or be dealt damage.

A creature can be dealt an amount of damage greater than its toughness. For example, if Brash Taunter is dealt 3 damage, its middle ability deals 3 damage, not 1, to the target opponent.

If your life total is brought to 0 or less at the same time that Brash Taunter is dealt damage, you lose the game before its middle ability goes on the stack.