When encountering legendary Pokémon like Rayquaza, Kyogre, Groudon, or the Regis, the goal is to catch them, not defeat them. Lower their HP to red, inflict a status condition (Sleep or Paralysis are best), and then throw Ultra Balls. Save before each encounter. Having a Pokémon with False Swipe (leaves 1 HP) is incredibly useful. Be patient, as catching them can take many turns.
