A creature's training ability triggers only when both that creature and a creature with greater power are declared as attackers. Increasing a creature's power after attackers are declared won't cause a training ability to trigger.

Once a creature's training ability has triggered, destroying the other attacking creature or reducing its power won't stop the creature with training from getting a +1/+1 counter.

A creature “trains” when a +1/+1 counter is put onto it at as a result of its training ability resolving.