These are my notes, if you've run the game you'll probably have no trouble deciphering them! If you've not, then watch the video attached to my leaderboard run :)

I have tested teleporting vs flying and I think that I've picked the fastest for each part, but let me know if I'm wrong!

• Enter Scande and examine the elevator
• Warp to Tunlan and get Rod5
• Leave Tunland and fly East to Auria, sell the Andtx9 then buy 12 MRBL1 and 3 Worm
• Fly south past the desert, equip Ryu with Rod5 and worm then fish at the fishing hole
• Warp to Spring, get the parts from the house south of the Dragon Shrine and then fish in the pond for Dragon AR
• Leave Spring, fly NE and fish at the spot west of Gust
• Fly NE again and fish at the spot west of Agua
• Fly SE to the first dragon shrine
• Equip all the Dragon Gear, change to backrow then AB through (hope for a slam so it's done in 2 turns!)
• Fly west and speak to the weapon collecting woman
• Fly south the weapon collecting man, and keep going back and forth between them until you get the I.Claw
• Fly West to Gant, go up to the top of the town and get the Parts fixed
• Leave town and fly slightly west to the next dragon shrine
• THDR dragon, MRBL1s
• Leave and fly SW to Scande
• Fix the elevator, go up and speak to not-Jade. Exit with Bleu
• Warp to Drogon, buy 15MRBL3 and 4 Cure (for safety, you can be a risky fellow and buy 2-3 if you want to shave the frames)
• Fly NW to the 3rd Shrine
• FirDrg. USe the 2 MRBL1s that are left in the first slot, then organise your inventory moving the other 3 to the first slot, then the MRBL3 and Cures to other slots on the first 2 rows. I like to have it MRBL1, Acorn, Cure row 1, MRBL3, MRBL3 row 2. Use the other MRBL1 to win. You won't need to heal unless he gets 2 slams, but that happens rarely.
• Fly east to the water cave and get Agni. Use 1 MRBL3 7 steps in, another as your turn South on the 2nd floor. Exit with Bleu
• Warp to Tunlan, get the D.Hrt
• Fly SW to Scande, go through until you defeat Zog (Agni, AB. Use a cure if you fall under about 200 if you wanna be super safe)
• Mash through cutscene, leave Scande and warp to Gramor
• Take Mogu to see the digger and learn to use the I.Claw
• Leave Gramor and fly NE to Agua. Put Karn in front
• Scale Agua until you find Sara
• Karn use the D.Hrt (should be in Row 1 thanks to the MRBL organising earlier), Mogu atk, others defend.
• Continue through, get through the cutscene until you exit Drogon
• Fly SW to Scande, switch to Mogu when you land and dig in
• Play through as normal, Agni and AB makes short work of Goda
• Continue the usual way to Jade and initiate a fight
• Pray to Myria that he doesn't use shock, turn into Agni then AB through. Expect to use one cure, being aware that there's a small chance he could hit you for 400 with thunder.
• If he uses shock you CAN use the WtrJr to bring back Ryu and get back into Agni, but the timeloss is a killer, and he could just kill the user. If even one person is dead Ryu can't transform.
• After the battle open the menu and fill Ryu with delicious acorns
• Go down the lift and face Tyr
• Use Agni then AB first form
• Use Agni and AB 2nd form. you'll probably use 2 cures here as I don't think you can do it with 1 without amazing luck.
• Grats