Notes & Combos
This deck is Psychic End Punisher turbo, going 2nd OTK. This deck's main win condition is getting Psychic End Punisher (PEP) on your board as soon as possible with your LP as low as possible. The line towards PEP is 7 + 4 = 11. That is the point of level 7 Tenyi's and the generic level 7 Synchro mnonsters. (Ancient Pixie Dragon is not actually needed; any level 7 Synchro monster will do that can be summoned.) The super budget version only needs one UR, which is PEP, but having certain SRs/URs would help the win percentage.
If you do not see a line of play towards PEP, you are going to have to play weakened version of Swordsoul Tenyi while going second and hope you can win with that or have enough gas for the fourth turn while still surviving on low LP.
This deck is using what SR/UR I had lying around, so I did not have to craft any new SRs/URs. If I were to make this build better, I would add a third Ecclesia and a third Emergence. I would max out on Upstart Goblin and Chicken Game since that increases that LP difference for PEP. I would add Power Tool Dragon to the extra deck, so I have the level 7 I need, to not only go into PEP, but to get Psychic Blade for an easier line towards OTK. Most trap cards are too slow for this deck's main win condition, but having Red Reboot can help secure certain instances where the trap cards are too strong while bolstering PEP's attack.
The cards I would remove first are Ash and Nibiru. They help to prevent first turn opponents from setting up a board that is too hard to break, but the Kaijus and Lightning Storm can help out with that (though I sometimes did not draw the out).