Have you tried something similar to this from for example a live OS or rescue boot menu from a linux installation media (cd dvd usb etc...)
$ sudo cryptsetup luksOpen /dev/sd<yourEncryptedDiskId> <aNameThatwillBeCreatedIn:Dev/mapper>
Like for exemple :
$ sudo cryptsetup luksOpen /dev/sda tmpData
and then
$ sudo mount /dev/mapper/<TheNameUsedEarlier> /mnt #wherever you want
so as in the exemple :
$ sudo mount /dev/mapper/tmpData /mnt #wherever you want
now you can access your data.
Now that what needed to be done is done you can close the device :
$ sudo umount /mnt
$ sudo cryptsetup luksClose tmpData