What are the required stats for a run in this game? Whether it be eevee or Ted. I was just wondering.

for eevee, you are wanting to aim for a 17-18 sp.atk with a modest,mild or rash nature, and for teddy you wanna aim for 23 atk and 15 speed minimum

Notes on Ursa for purification purposes (yellow cells are unlocked) https://docs.google.com/spreadsheets/d/1oiRPfltss_2t2Io06rxkOBn3RZA5QMwba7qONkgI1VA/edit?usp=sharing

Of course, running 15 speed on Ursa is risky according to the PSR marathon XD run from this year because you wouldn't be guaranteed to outrun certain pokes you would be guaranteed on if Ursa were 16 speed or faster. Any of those pokes that are notable enough are mentioned in that run.