When Batterskull enters the battlefield, its living weapon ability will trigger. When this trigger resolves, a 0/0 germ token creature is created and the Batterskull will become attached to it. Each of these steps is followed in order, so the germ will be a 0/0 creature for a short time and then become 4/4. The germ remains on the battlefield because these two things happen during the resolution of the living weapon ability, and state-based actions are not checked until after the trigger completely resolves.

Because the creature enters the battlefield as a 0/0 creature, this will trigger Mentor of the Meek‘s ability. Triggered abilities can trigger anytime that their trigger condition is met, regardless of how long this condition remains true. It doesn’t matter that by the time the living weapon trigger finishes resolving or when the Mentor of the Meek trigger goes on the stack that the germ is a 4/4 creature.

This is also true for the other living weapon equipment that can raise the equipped creature’s power by three or more, such as Necropouncer and, under certain circumstances, Bonehoard.