I had a similar issue, 0.8mm holes, but through stainless steel, HSS drills barely touched it, so I went for PCB drills, these are tungsten carbide and can be bought in 0.1mm increments from 0.1mm, they work in a power drill (dremel) at speed and go through stainless steel like a knife through butter, at times I have a little archimedes drill handle that you push down to rotate the bit manually.
The only reason I recommend the pcb drills is that they have quite a short bit (10mm) that then fattens out to hold in the drill, this allows for less breakages.