So I consider myself intermediate/beginner level at guitar. I just tried learning the stairway to heaven solo (I know, but i'm new to soloing) and it took me about 4-5 days to learn. The problem is, it sounds very sloppy. I've been practicing it at a slower tempo, and have been focusing on each part individually, but it still sounds the same. Any advice? How long does it usually take you to master a solo?
I rarely learn other people's solos but in learning solos I've written the real key is figuring out why it sounds bad. Are you not striking the strings well? Are you fretting with too much or too little pressure, causing either sharp notes or fret buzz respectively? Are you not muting properly and allowing open string noise or sympathetic vibrations? Are your bends in tune? Is your vibrato controlled and appropriate for the situation?

You need to analyse what you are doing wrong, the best way to do that is to record yourself and listen with a very critical ear; doing it while you're playing is somewhere between difficult and impossible.

If you want more help from us here you'll need to provide a recording so we can give you more specific advice.
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How long does it take to master a solo? Years, years of practice and you'll maybe master it, a big reason it sounds bad is because you're a beginner, most of what you play will sound bad but that's the reason we keep going, to sound better each time but yeah record yourself, the amount of times i've played something and thought "that was great" and then listened to it back and it was terrible is staggering but recording will help you nail down what is the real issue but upload something for us to hear
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If you're at a beginner / intermediate level and this is your first solo, it's going to sound sloppy. You'll probably need to learn quite a few solos before you've worked all the aspects of your technique up to the point where they start sounding good.

Slow it down using any of the DAW programs these days, practice it at a tempo you're comfortable with, and take careful note of the parts that are giving you problems and work on them separately. Then gradually work it up to full tempo.
Be careful concerning your bends. How long they last, are they in tune, etc. Then, play it with a backing track to make sure the rythm is good.