Step 1. Activate Trade-In, Discarding Galaxy-Eyes Photon Dragon and drawing 2 cards
Step 2. Special Summon Photon Thrasher using its effect
Step 3. Special Summon Photon Vanisher using its effect
Step 4. Activate Photon Vanisher's effect, adding Galaxy Eyes Photon Dragon to your hand
Step 5. Link Summon Galaxy-Eyes Solflare using Vanisher and Thrasher
Step 6. Using Solflare's effect, add Vanisher back to the hand
Step 7. Activate Galaxy Transfer, Paying 2000 Lifepoints and special summoning Galaxy Eyes from the graveyard and Galaxy Eyes Afterglow Dragon from the deck
Step 8. 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