fsck -fy hangs on Checking catalog file + issues booting (MacBook)
When you can't get a clean run of fsck (which you might need to let run for a handful of hours) - then it's time to make a decision:


back up what you can/need to and erase the volume
seek other software options to attempt repair


In my expereice, if you don't have lots of IO errors (-B option for fsck_hfs) then the erase will restore full function and you can reinstall the OS and restore from backup. I've also not had much luck forcing fsck_hfs to rebuild parts when the plain /sbin/fsck -fy fails - but you could get lucky there with an unusual corruption pattern on this drive.

The second option doesn't have great promise. Disk Warrior seems to be one of the decent utilities to try when fsck won't work - but unless you have lots of specific corruption issues - the time you spend wiping and reinstalling usually doesn't outweigh the cost of that software. It also may or may not work. If Disk Warrior also fails to repair or rebuild the catalog, you're back to the decision point - wipe or escalate to even more expensive / specialized support like opening an engineering ticket with Apple or someone that's able to dump the filesystem structure more deeply for analysis.