The key thing here is to know the actual partition that is encrypted.
Often in Linux Mint's installer that ends up being partition 5 or /dev/sda5
sudo cryptsetup luksOpen /dev/sda5 anynamehere
You will then be prompted for your irrecoverable passphrase:
Enter passphrase for /dev/sda5:
If all goes well it won't say anything further. If it says ""No key available with this passphrase." it means you have entered the wrong password.
How to mount
The above command will create a device based on the third argument that you passed to cryptsetup (anynamehere) in the above example.
So you would see i/dev/mapper/anynamehere
From there just go ahead and mount it (assuming it is not using LVM-read on if you are).
mount /dev/mapper/anynamehere /mnt/crypteddisk
To make it more practical perhaps you are trying to modify or fix your OS.
From here if we were using many OS's we would then do an "lvscan". It will then show us the LVM volumes and you can then mount the vg-root to /mnt
You can then do something like this:
mount /dev/vgname/vg-root /mnt
#use the bash script to mount /dev /proc and /sys to your /mnt (chroot) root dir so stuff works when you chroot
for mount in dev proc sys; do
mount -o bind /$mount /mnt/$mount
#now let's chroot in!
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