Alpha Deathclaw

Menace, trample
When this creature enters or becomes monstrous, destroy target permanent.
{5}{B}{G}: Monstrosity 4. (If this creature isn't monstrous, put four +1/+1 counters on it and it becomes monstrous.)

Fallout

Menace, trample
When Alpha Deathclaw enters the battlefield or becomes monstrous, destroy target permanent.
{5}{B}{G}: Monstrosity 4. (If this creature isn't monstrous, put four +1/+1 counters on it and it becomes monstrous.)

Menace, trample
When Alpha Deathclaw enters the battlefield or becomes monstrous, destroy target permanent.
{5}{B}{G}: Monstrosity 4.

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.