I used to try to improve my pull-ups for a long time with not particularly good results. I switched to doing chin-ups, and I'm starting to see actual improvements in lat strength now.
Then again, I also started doing deadlifts and barbell/dumbbell rows so that might have had something to do with it as well
Can't speak to the whole routine but for pullups I'd suggest negatives first and then banded pullups. Some gyms even have weight assisted pull up machines
I have a weighted machine in my gym but most ppl dont recommend them cause the core isnt actvated
Pullups are not a core exercise, so don't worry about that. The assist will get you to unassisted pullups
If you wanna do X, practice X. In fitness, for almost anything, there's an easy version of the thing. In this case, negative pullups.
Ok I dont think I can do them yet...
You can always do negatives. Put a bar around shoulder height, stand straight, grab it, and slowly lift your legs. You will start to slide down because you can't hold your bodyweight without putting your legs on the ground. So you'll slide down. Congratulations, you did a negative pull-up.
Negatives are just starting at the top of the bar and trying to slow how quickly you drop down. If you can't do that, then there probably some other fitness priorities you should be focusing on instead.
This was how I was able to do them. It took about 10-15 days of trying before I was able to do one. Once I could do one, I was quickly able to do three. I was topping out at 10 after a month.
I was also losing weight quickly, and had gone from 210lbs to something much smaller. I didn't have a scale.
Start with just hanging and lowering yourself down slowly.
One way to start is to have someone or some thing hold your legs up while you do them, assisted pull-ups. Each time after, try to do as many solo pull-ups as possible, followed by assisted pull-ups.
Continue this routine until you are able to do them comfortably up to a specified amount.
as a side note, make sure your checking your posture and shoulder flexibility as you do it. many people do them with an arched back. you should be able to hang straight down through the whole motion while doing them. that's the part i struggle the most with.
set your back flat against the wall and slowly raise your arms up from the side keeping them flat against the wall. if your back or arms need to lift off the wall at all as you reach all the way up you should work on your flexibility as well.
There's no problem with doing pull-ups with an arch. It's just a different variation that uses a different set of muscles. Most people find it easier to pull with an arched back.