I avoided Zhuyin like the plague and stuck with Hanyu Pinyin until I came here. But here, Zhuyin’s necessary.
I eventually learned it by forcing myself to read two pages of a short and simple, high frequency vocab, children’s book. I read it three times a week–about 20 minutes each time–for four consecutive weeks. You’ll probably make more progress if you study more. It’s easier if you get someone to record their voice for you so you can read along with that. Just make sure you pick someone with a more standard/northern pronunciation so it will match what you’re seeing. I usually ask my friends to do the recording twice: one slow enough for me to read with while I’m getting used to forming the words, and a second time at the normal speed so I can practice fluency.
Good luck!
[Edit: I realize this is a lot less than 20 hours, but this isn’t perfect knowledge either. I’m not as stable as I’d like to be. Sometimes, if I don’t read for a week or two, I forget the sound of some the less frequent characters symbols.]