I see some people don't know the jist of what needs to be done, so here's what you would need to do generally, whether or not it's a speedrun.
To get to and kill the Celestial Champion, you'd need to:
1. Go to ruins and get a Star Caller Staff and Deconstruction Staff.
2. Do the Moon Stone Event and convert the Starcaller staff into a Moon Caller Staff. The Decon staff is used to get the Opal Gem from this staff.
3. Turn the power on in the archives and get the Astral Detector BP from the puzzle room for the Celestial Sanctum Pieces.
4. Do the Hermit Quests. You MUST complete Pearl's house, which requires Cactus Flower, which requires the Summer season. (Have fun with the Cookie Cutter Shell RNG btw, since you need 10 of them, unless you do dupe strats with the cookie cutter hat). Completing Pearl's house counts as 3 tasks, and you need 10 tasks total, so you need to do 7 of the following tasks.
Each of the seasonal fish count as their own task. If I remember the code right, the seasonal fish must be heavy as well (I'm on mobile so I'm not checking anytime soon).
5. Kill Pearled Crab King.
6. Socket all three celestial Pieces (Altar, Crown, & Sanctum) to spawn the Moon Storm event.
7. Complete Wagstaff's minigame 3 times for the needed 3 Restrained Static.
8. Get 15 Moon Gleams, 30 Infused Shards, and the Celestial Orb. With bad enough RNG, the orb might spawn as late as day 60 (yes, it happens). For the Infused Shards, you've got 90 secs to get that to the Lunar Island to complete the Containment unit. Use either bundles, gift wraps if you turn Winter's Feast on, or telelocate yourself on and off the island how many times you need to.
9. Kill the Celestial Champion. I don't know if 25% speed bonus is required for this fight. If it is, get a Magi and/or cane or be Mighty Wolfgang or Wortox, whatever way you deal with phase 2 or the boss in general.
You figure out how you're going to kill the bosses, I think I've written enough :>