Pokemon has never been beaten without taking damage, for good reason. It's an absolutely impossible challenge: you'd have to be an absolute idiot to even make an attempt.
Let's do it.

Special thanks to Pikasprey: Pokemon challenge runs personified!
   / pikasprey  

This run was streamed live on my Twitch channel. If you'd like to join the funtimes, check in at
  / gamechamp3k  

Plus, if you'd like to watch the original stream archives, they'll soon be uploaded to the Let's Strem channel:
   / letsstrem  

If you'd like to support the channel and make possible shows like VG Myths, Region Freedom, Dumb Fun Gaming, and A Complete Review, please consider backing on Patreon~
  / gamechamp  

Fellow Youtubers
Ceave Gaming:    / ceavegaming  
Pikasprey Yellow:    / pikasprey  
Smallant:    / smallant  
Skip the Tutorial:    / skipthetutorial  
Nathaniel Bandy:    / nathanielbandy  
Mayro:    / @mayrosmm  
Nick Robinson:    / babylonian  
Still Gaming:    / stillgaming  

Media Sources
Pokémon Blue Version
Pokémon Stadium 2
Bulbapedia
Strategy Wiki
pokemonspeedruns.com
The Legend of Zelda: The Wind Waker
Harmoknight
Music from KH Insider