Red is drunk. He likes to steal drugs from Walmart, and use them. He especially likes alcohol. So, basically, he is the link that is drunk.
He is the only link not to be based off a Kirby. Green is based off of white kirby. Blue is based off of Blue Kirby. And Purple is based off of the GKAR Purple Kirby.
Red Link does not appear on the SMSB roster, but randomly appears in matches when Green Link is selected. This is because he is a model swap of Green Link.
Reds up special custom and defense stat in SSB4 are said to be that way because he is drunk.