So I followed along with the video up to the portion where you add TakingDamage update. I followed along exactly as the video instructed but it seems to be registering the void TakingDamage as being entirely incorrect. I recently updated Unity so maybe that could be the problem but I'm not sure I'm skilled enough at scripting yet to fix this on my own.
You added a semicolon after the "void TakeDamage()" that's why it's giving you an error.