Mythril Mine isn't one of my favorite places in Final Fantasy 7: Rebirth, mainly because of the way the environment is shared. If you're stuck trying to find your way back up as Barret and Red XIII, this is the guide for you.
Final Fantasy VII Rebirth How to Get Through Mythril Mines as Barret
To leave the bottom of Mythril Mine, you just have to remember to keep going up. Let's start in this big room with too many rooms to explore.
Go to this eastern point on the map. Look for rocks to climb and climb to the left. If you climb to the right, you will come to a mineral deposit.
Once you reach the next "floor", have Barret blow up all the crystals until you see more rock ledges to climb. They're a bit hard to spot, to the point where I missed them so many times in my playthrough.