I just claw everything.
If you don't want to do that (most people don't), there still are different tricks that might help you.
Custom controls is one way. The control scheme I have heard of most often is setting Z to jump and using any of R/L+A, X/Y, R/L for grabs. The second to last post right now in the general discussion thread actually recommends doing this and apparently it makes many things much easier once you're comfortable with the new controls. Relearning the control scheme is strange at first and takes some time, but if you intend to ever optimize your controls for easier gameplay, you should do it as soon as possible, i.e. now.
If you also don't want to do that you can try to operate the C-stick with the lower part of your thump. Neon does something like this (see above). Requires less relearning of controls, but feels the most straining to me personally. Might just be a matter of preference though.
Finally, should nothing else work for you, you can also just train more. It'll take a while, but if you just keep practicing your ATs every day, you'll get fast enough eventually.