I managed to get 1000 everywhere once again this time using a custom Charizard with a vampire drawn badge, an all-around trade-off agility badge, and an X attack (no secondary effect, but large attack boost), and with Dragon Rush instead of Flare Blitz. Powers are given him were spinning blades level 3, Ore Club level 2, and heavenly light level 2. Spinning blades is so useful against horde of enemies (especially against Souflees, seriously using this power in a Souflee fest is pretty much necessary to get 1000 everywhere), Ore Club is just OP and can kill even the most powerful enemies like Clubberskulls in less than ten seconds, and heavenly light is a situational helper in some challenge chambers (easy survive and normal or hard break the targets).
Very early I had the opportunity to find a Souflee fest and thanks to spinning blades I killed 8 or 9 of them... This gave me huge offensive, mobility and defensive boosts which were extremely useful for the rest of the run. I also did it with The Mysterious Murasame Castle Medley medley, such a fitting music for Smash Run, it should have been a default track imo.
I think Charizard is one of the best characters to use in Smash Run. Good mobility thanks to high dashing speed and double midair jump (I know they kinda suck but once you get some jump stat boost they actually become useful), heavyweight which means high survivability, fire to easily deal with polar bears, up throw gives mobility utility, and Rock Smash is a powerful attack which gives launch resistance, making it particularly useful against powerful enemies like Bulborbs.
Now that I managed to get 1000 everywhere with ZSS and Charizard I'm wondering who I'm going to use next for this challenge. Guess I'll try it with either Captain Falcon or Mario next time.