{5}{R}{R}: Monstrosity 1. (If this creature isn't monstrous, put a +1/+1 counter on it and it becomes monstrous.)
When this creature becomes monstrous, it deals 2 damage to each opponent and each creature they control.
An ability that triggers when a creature becomes monstrous won't trigger if that creature isn't on the battlefield when its monstrosity ability resolves.
Monstrous isn't an ability that a creature has. It's just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.
Once a creature becomes monstrous, it can't become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.