Whenever a creature an opponent controls attacks one of your opponents, double its power until end of turn.
{X}{X}{R}: Monstrosity X. (If this creature isn't monstrous, put X +1/+1 counters on it and it becomes monstrous.)
When Death Kiss becomes monstrous, goad up to X target creatures your opponents 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.
To double a creature's power, it gets +X/+0, where X is its power as that ability resolves.