Step 1. Special Summon Galaxy Soldier by discarding Galaxy Eyes Afterglow Dragon
Step 2. Activate Galaxy Soldier's effect, adding Galaxy Wizard to the hand
Step 3. Normal Summon Galaxy Wizard
Step 4. Activate Galaxy Wizard's effect, tributing itself to add Galaxy Transfer to the hand
Step 5. Activate Galaxy Expedition, Special Summoning Galaxy-Eyes Photon Dragon from the deck
Step 6. Link Summon Galaxy-Eyes Sol Flare Dragon using Photon Dragon and Galaxy Soldier
Step 7. Activate Sol Flare Dragon's effect, returning Afterglow Dragon to the hand
Step 8. Activate Galaxy Transfer, Paying 2000 Lifepoints and Special Summoning Galaxy Eyes from the graveyard and another galaxy eyes(if going first) or afterglow (if going second) from the deck
Step 9. XYZ Summon Number 90:Galaxy Eyes Photon Lord (if going first) or Number 62: Galaxy Eyes Prime Dragon (if going Second)

If you summoned Number 62:
Enter Battle Phase, and attack a card the opponent controls.
Activate Prime Photon's effect, detaching an Afterglow Dragon and increasing Prime Photon's attack by 1600
Activate Afterglow's effect, Special Summoning another Galaxy-Eyes Photon Dragon from the deck, and double Prime Photon's attack
Attack for a lot of damage