You don't need to predict in Brawl so much. It's playing safe mostly. Zelda's movement is really limited, so I don't know how safe she can be.
Compare your options with each of your opposing character's. That's what I do. For example, Meta Knight. His options are dashing into shield, dashgrabbing, Fair, Ftilt. Dtilt isn't as important because if you watch for Ftilt, Dtilt is less likely to hit anyway (range difference). Same with grounded Shuttle Loop. I play Fox on MK.
What I do against that specific character, is full hopping. It's safe on MK's walking, dashing and short-hop approaches, and if he decides to do an approach, Fox can fast-fall quickly enough to punish with a Dair (fastest faller in the game, this is an advantage). Dashing and shielding as Fox is quicker than as MK, so I abuse that also. Dash, shield, grab.
If they shield, I can stall them out with my air-jump, and footstool shields also to allow even more stalling. A bit of stalling deteriorates a shield enough for Dair to shield-poke. Short-hop bair beats impatient Dsmash approaches/KO attempts since it hits above Dsmash's hitbox.
Notice your opponent's options. During matches, once you have practice, you can start noticing your opponent's tendencies to do some things more than others.
The most important thing is being safe and being patient. I've never seen Zelda win. So go ahead...I also recommend playing 2 or 3 characters. It doesn't matter much which ones, but it just makes you cooler and allows counterpicks. I go MK+Fox, as I stated.