This is a problem that arises when one has an encrypted file-system. It is caused by a bug that has been fixed but has re-appeared. The symptom is that after entering hte passphrase for your encryypted root fs you get the message: Failed to connect to lvmetad. This will repeat many time suntil you are dropped into a busybox shell.
If you leave the machine to sit for a while and then exit the shell with ^D, it will boot. The workaround is:
edit /etc/initramfs-tools/conf.d/resume to read "RESUME=none"
run sudo update-initramfs -u
reboot
This will have the effect of disabling your swap partition, but you will at
least be able to boot with no problems.
See
Failed to connect to lvmetad"
You can also turn off the use of lvmetad completely by editing /etc/lvm/lvm.conf and changing use_lvmetad from 1 to 0. You also need to run update-initramfs afterwards.