Instructions
Assemble the team that you want to fight Winona. If you have a fire Pokemon, like Ponyta or Blaziken, include that Pokemon in the team. Teach the fire Pokemon a rock-type move, if possible. Include an electric Pokemon or two, and an ice Pokemon, if you have one.
Train the team to at least level 30. If you train the team to level 34 or above, you can beat most of Winona's Pokemon without any trouble. Winona's Pokemon range from level 30 to level 33.
Strike Winona's Pelipper with an electric attack, like Spark or Zap Cannon. Pelipper's combined water and flying types make it very susceptible to electricity. When Winona calls out her Swellow, take it out with electricity, as well.
Switch to your fire Pokemon when Winona calls out Skarmory. Skarmory is both steel and flying-type, so electric moves are not effective on it. Instead, blast it with your Pokemon's fire attack. If you taught the Pokemon a rock-type move, you can use that move instead.
Use your fire Pokemon's rock move against Altaria, a dragon and flying-type Pokemon. If the Pokemon does not know a rock move, switch to an ice Pokemon. Ice attacks work well against both dragon and flying Pokemon. If you have no rock or ice moves to use, use electric attacks.