Well, it depends on how technical you'd want to get in the terms of death. For example, falling off one of the islands when messing around, or getting hit by a Guardian, which I don't count anyhow, since you don't run out of hearts. With that logic I'll just say that I have died about 10 times, more or less. Most of this was due to Boss battles, such as Tentalus (oi), or enemy battles, like the Lizalfos. They can be pretty tough both defensively and offensively. Since they block most of my haphazard swings they are much riskier than others. Their fire-breathing is also a factor which requires more precaution. So...I merely need be wary about them.
And circa 10 deaths for me, not counting saves by fairies or Potions. It'll probably increase as I chance the Boss Rush Mode and eventually Demise.