As always I would recommend being on the overly cautious side with hardcore characters. I highly recommend being at least level 25 before tackling Belial. This isn't too hard to achieve if you run the Zoltun Kulle quest for the xp reward and you can get a little extra gold along with it (teleporting to him and killing him shouldn't take longer than a minute).
Finally, builds and gear makes a big difference, but you can 'test him out'1 in the first stage. If your health drops anywhere below 50% before he transforms, I'd say its a safe bet the second form is too dangerous to attempt.
For Azmodan you'd want to be in the mid 30s and to be safe, level 40+ for Diablo.
1 Build yourself a similar softcore character with similar gear to learn the boss's patterns and whether or not your level is good enough to take him.