since your unable to get manjaro to boot and you think its mint's grub2 (iirc, manjaro would of replaced this with manjaro's grub, but i could definitely be wrong) start by rebooting to the live usb installer so you can use manjaro-chroot to access your installed manjaro system.
do the following:
-boot up the live usb install desktop
-connect to network
-open terminal and input following:
sudo manjaro-chroot -a
you should now be at a user shell looking somthing like this:
==> Mounting (ManjaroLinux) [/dev/sdb2]
--> mount: [/mnt]
--> mount: [/mnt/boot/efi]
[dglt-4 /]#
once your there, you can update mirrors and do a full update:
pacman-mirrors -g
sudo pacman -Syyu
could you also include:
lsblk -f
to see how your drive is partitioned