the librt.so.1 share liberary missing after update or remove some ubuntu application, the below is a way to rescuse ubuntu boot up failure issue.
1.Boot from installation medium(live cd)
2.Mount your problematic Ubuntu root filesystem with file manager by clicking on the drive icon in the Devices section
If unsure which partition to mount then check it with Disks (gnome-disks) utility and mount it from here:
4. go to download the missing liberaries by here (debian packet searchig website) or http://http.us.debian.org/debian/pool/main/g/glibc/
#mkdir ~/tmp; cd ~/tmp
#wget http://http.us.debian.org/debian/pool/main/g/glibc/libc6_2.31-13+deb11u3_i386.deb or
#wget http://http.us.debian.org/debian/pool/main/g/glibc/libc6_2.31-13+deb11u5_i386.deb
#wget http://ftp.us.debian.org/debian/pool/main/g/glibc/libc6_2.31-13+deb11u3_amd64.deb or
#wget http://http.us.debian.org/debian/pool/main/g/glibc/libc6_2.31-13+deb11u5_amd64.deb
#dpkg -x libc6_2.31-13+deb11u3_amd64.deb /media/to/your/topdir of problemic rootfs/
Check that above operation do not have errors and then reboot.
