Instructions
Teach one of your Pokemon a fixed-damage move. These moves include Night Shade and Seismic Toss. This makes defeating Lucy's Shuckle very easy, as it has extremely high defense but low HP.
Train an electric Pokemon, such as Manectric, Magneton, or Jolteon. These will easily be able to defeat Lucy's Milotic, which is weak to Electric attacks.
Train a strong Psychic- or Ground-type Pokemon to defeat Lucy's Seviper. The Seviper is a Poison-type, so it is weak against Pyschic- and Ground-type moves. Good Pokemon to train are Alakazam and Metagross. Metagross is the best choice because it can learn Ground- and Pyshic-type moves and it is immune to Poison-type attacks. It is also a very strong Pokemon.