Yesterday when I updated the system it didn’t went through due to a conflict when updating the nss package (if I recall correctly). The error message was something about that the file (which I don’t remember the name of) already exists on the system. I didn’t manage to solve it and just left it.
When I later did a shutdown the system hanged and I had to force turn off the computer with a long-press on the power button. Now it won’t boot anymore.
You will need to boot from the live usb and do a repair. The guide @halcek linked is good, just doesn’t cover luks or lvm, which I noticed your using.
First up find out what device and partitions you’ll be working with
lsblk -f
Encrypted partitions will need to be unlocked before they can be mounted, I noticed the name is default “cryptroot” from your pic, this is also needed.
cryptsetup open --type luks /dev/ROOT_PARTITION "cryptroot"
Now mount the root partition (for encryption this needs to use the /dev/mapper/NAME)
mount /dev/mapper/cryptroot /mnt
This next step (mounting boot partition)ONLY applies if you use a seperate boot partition
mount /dev/BOOT_PARTITION /mnt/boot
Once everything is mounted you need to chroot into the system
arch-chroot /mnt
From here you can run an update as @halcek posted, I would also run a couple other commands
pacman -Syu --overwrite /usr/lib\*/p11-kit-trust.so
# rebuild initramfs for all installed kernels
mkinitcpio -P
# update grub config -- ONLY if you use grub
grub-mkconfig -o /boot/grub/grub.cfg
Once finished you need to exit the chroot
exit
Then reboot.
Lemme know if I was unclear or if you have any issues.