If a Monster reaches 20 Victory Points and 0 Life in the same turn because of a Power card, they are eliminated. You must survive your turn to win. If all Monsters are eliminated at the same time, everyone loses.

This is stated in the example on page 6:

"If you reach 20 and reach 0 in the same turn because of a Power card, you are eliminated. You must survive your turn to win. If all Monsters are eliminated at the same time... everyone loses!"

Source: page 6

Source: Core Rulebook (pp. 1, 2, 3, 5, 6)