Set up the work piece so that it's comfortable and safe to work on and secure it to allow you to exert pressure without it shifting.
Choose three or four
new bits in 0.5mm increments, the largest being the same as the inside diameter of the back nut.
Start with the smallest drill bit, flood the area with oil and run the drill at very slow speed, between 120 and 240 rpm. Push hard and straight on the bit. Too fast and/or too light and you'll burn the drill.
Once you are through work your way up through the bit sizes.
Don't use cheap Allan keys on your bolts in future!