How can I play Mystic Sanctuary and not auto-lose to Boil?
The main threat of Boil is that it is a single card that can destroy multiple Islands at once. If you are in a situation where you have multiple Islands to get destroyed, you should be able to have some of them untapped. So you can just handle it like any other threat and play regular countermagic like Negate or Mana Leak or Cryptic Command, and keep mana available when your opponent is threatening Boil.