If you want to obtain X skill you should be doing the progression for X skill. For example, if you want to obtain X skill, you should be doing the muscle up progression.
Doing "BICEPZ WORK BRAH" is not going to get you anywhere, except looking stupid.
If you're at the point where you can't do a muscle up, isolating muscles is not going to help you significantly get stronger to do it.
You need to be doing full range of motion compound exercises like pullups and rows. Maybe add in some bicepszzzzzzz work at the end but it's just supplemental to main movements.
That's what I mean. Maybe Matt is asking for progressions.
I'll try and give you advice on what worked for me.
If you can't do pull-ups yet:
Do chin-ups, ya know find a bar or a tree branch that's high enough, and pull yourself all the way up once, a jump to assist you is fine. To me the difference between pull-ups and chin-ups is that chin-ups only go halfway down. These are easier because your muscles need to apply more force to pull you up if your arms are extended.
Also, I started off with an underhand grip, ya know palms facing your face. These were just easier for me I don't know why; but I soon learned that overhand, palms facing away from you, is better, because you're never going to do an underhanded climb-up. Even though these might be a bit harder, you should try and do these as soon as possible.
Um.....once you've got a good enough number of chin-ups down start pull-ups (overhand as well).
I try and do pull-ups as explosively as possible. I don't mean pull-up real fast, drop down real fast, and then use some of that momentum to pull yourself back up. I mean pull yourself up as quickly as possible, but using only your arms, none of that kicking your legs to get yourself up crap. Then go down normally.
My reason for doing this, and this is just a hunch, I have no proof of this but my own logic, is this: a lot of movements in parkour need explosive force to be quick right? Including climb-ups. So I'm guessing exercising the same way should help you more.
Like I said before, I'm no expert in exercise, far from it. But that's what has worked for me and I could do about 5 muscle ups, just gotta work out more and I'm on my road to ten.