How can someone defeat Galaxy Eyes Photon Dragon and what cards can negate the Galaxy Eyes to be destroyed?

Galaxy Eyes Photon Dragon has absolutely no protections against being destroyed, apart from its battle phase banish ability, which can only be done at a specific part in the battle phase.

So any monster destruction will do it - Exiled Force, Fissure, etc.

You could use a card like Divine Wrath against its Quick Effect, if it tried to banish itself in the battle phase to escape destruction from a card like Mirror Force.