First Phendrona, now you, asking for Brawl tips. xD Flattering!
Learn how to air dodge. If you don't, then you will be juggled mercilessly until you die. Usually people have some sort of predictable pattern that they use to attack while in the air, so try to learn that pattern (it's different for every person, of course), so you can predict when they'll attack and successfully evade.
...I never use the Ice Climbers so I can't give any character-specific advice, sorry. D: