Couple of things -
1. A paper hole punch does wonders for near 1/4" holes in a mint tin. You may have to auger them out slightly, but as you've noticed - that's the issue.
2. Using a single drill bit the same size as your desired hole will almost always result in ripped metal. This happens on much thicker, quality cases, too. A step drill bit is standard equipment for many DIYer's. A step drill bit lets you enlarge the hole gradually, and the stress on the hole edge is much reduced. You can still do this manually, by starting small and changing out to progressively larger bits until the hole is finished - a PITA, but it can be done.
Lastly, and this is difficult with a Mint Tin - you should have a block of wood backing up the metal tin as you drill it. If you're lucky, all you need do is hold it tightly on the corner of a 2x4. There are other methods, but the important point is to make sure the tin is supported on the back side from your drill bit.