I die probably an average of 10 times minimum before beating certain bosses, yet I never run out of vials.
If you run out of vials on a boss - yer doing it wrong. Don't even bother healing the first time or two that you meet a boss.
If you have lots of echoes, use a mark and Awaken in the dream to spend them. If not - kite the boss for a few minutes and learn his attacks. After that, engage the boss - probably die - just don't heal. Do this a time or two more, until you can smack the boss down to about half health without healing - then you know yer ready to heal if need be, but you know you'll get the job done sooner rather than later, and you will only need to use a few vials.
would have driven me friggin bonkers if I didn't follow this rule.