"Don't get hit" is a very sound mentality.
I mean, you're going to get hit, but it's not the point.
Stay back and study your opponent, see what they do and when they do it, how they do it, and how well they do it, all while being non-confrontational. The key thing to getting better is being put in a situation, understanding what you did in the situation, and thinking of everything else you could have done in the situation to change that situation- good and bad.
Utilize the timer. You have 8 minutes (Or infinite minutes in Smash64) to beat your opponent, and you should use as much of that time as you can. Breath on the angel platform until it goes away, keep running from the opponent, and just try to get a grasp for how avoiding the opponent's attacks works. The more you study your opponent, the more opportunities you'll see.
Don't focus on capitalising on every hit or comboing for maximum percent every time. Instead try to set your opponent up so that they are in a bad position once you're done with your successive hits. Going for less damage but easier future hits is a very worthwhile proposition.
Understand how matchups work. Don't give a **** about the matchup numbers or charts thrown around, just focus on understanding the matchup on a personal level. What your character can do against theirs, and how you can avoid the enemies attacks yourself. Matchup experience is vital, untrainable, and needs to be understood through personal understanding. But it is vital none the less, and by far the most important part of the game (The only part of the game actually. I mean really, it's your character vs your opponent's.). If you don't have experience in hard matchups, personal or character wise, it's something you have to overcome on your own.
Know about trades, when you can take them, and how to afford them more easily. In Melee they can lead to important recovery situations, while in Brawl they can make for very interesting followups that don't work on normal hit.
Understand your mobility, stage control options, raw safety on hit, whiff, and block, and your moves' hitbox coverage and speed, to use your character the most efficiently and avoid your opponent most easily.
Basically,
All I'm trying to say
is
Just Play Homo.