Disclaimer: I finally tested the process myself. But I got the ideas initially from the posts in the old Manjaro forum, this one in particular.
When an installed encrypted system
- fails to boot to TTY (command line)
- or when the (correct) password fails to open the encryption after an update
the user might try to repair the system by chrooting it.
Chroot stands for change root and means to switch to a different root file system at runtime.
First find out the name of the encrypted device with lsblk -f:
~ >>> lsblk -f
NAME FSTYPE LABEL UUID MOUNTPOINT
sda btrfs 7d6dceec-fe31-4823-9740-0a02a4d20d1c /home
sdb
├─sdb1 crypto_LUKS 0c9ffa24-e245-4f01-a754-2fb86d9bb320
└─sdb2 swap dde5f6d7-a639-45df-af6d-7faac09c2eda
So here the name is crypto_LUKS and it is located in /dev/sdb1. If there is a separate /boot and/or /boot/efi partition (sda2 or sda3 respectively) like for a UEFI system you mount it after root. Then run the following commands:
su
cryptsetup open --type luks /dev/sda1 crypto_LUKS
mount /dev/mapper/crypto_LUKS /mnt
mount /dev/sda2 /mnt/boot # if the system has separate /boot partition (rare case)
mount /dev/sda3 /mnt/boot/efi # if the system boots in UEFI mode
mount -t proc proc /mnt/proc
mount -t sysfs sys /mnt/sys
mount -o bind /dev /mnt/dev
mount -o bind /run /mnt/run
mount -t devpts pts /mnt/dev/pts/
cp /etc/resolv.conf /mnt/etc/resolv.conf
chroot /mnt
Notice: This tutorial doesn't cover LVM, but you will see how LVs are set up in lsblk -f output and will be able to mount them using their /dev/mapper/... descriptor.
A viable alternative to manually mounting and chrooting is the following:
sudo mount /dev/mapper/crypto_LUKS /mnt
sudo mount /dev/sda2 /mnt/boot # if the system has separate /boot partition (rare case)
sudo mount /dev/sda3 /mnt/boot/efi # if the system boots in UEFI mode
manjaro-chroot /mnt
The command manjaro-chroot is part of the package manjaro-tools-base which must be installed for this method to work. (https://github.com/manjaro/manjaro-tools#6-manjaro-chroot)
Then you can install a new kernel or update the system or downgrade a package or run mkinitcpio. Examples:
pacman-mirrors -f 10
pacman -Syy
pacman -Syu
downgrade package_name
pacman -U /path/to/package_file
mhwd-kernel install linuxXY
mkinitcpio -P
sudo grub-install --recheck /dev/sda # if the system boots in legacy (MBR) mode
## for UEFI systems use the following command
sudo grub-install --target=x86_64-efi --efi-directory=/boot/efi --bootloader-id=manjaro --recheck
sudo update-grub
...
PS: Feel free to suggest additions to the tutorial, generalizations, special cases. And you can ask questions, too. But if the questions cannot get answered with one-two posts they will be moved to a separate topic. 
