Attack as any enemies as possible to get advanced moves quicker. Don't take on swarms of them though, especially Firebenders.

Increase attak damage:

Katara-Wear items with Life.
(Perhaps water or Lifebinder themed items)
Aang-Wear Agility items.
(Four Winds armor and trinkets work best.)
Haru- wear items containing Focus.
(Core items are a big help)
Sokka-Wear Strength items.
(He's definetly a "Soul Iron" kind of guy)

Note: The above are just suggestionz. Wearing all items of a set(Lemur, Badger, Bear, Unagi, Rain etc.) gives and extra boost.