Here's the winning strategy:
Use Gale's wind magic to turn the flower tiles into fire tiles and deal damage. Try selecting flower tiles that are adjacent to fire tiles. Once you are out of flower tiles, switch to using earth magic.
Use Inori's water magic to deal damage. Once you are out of water tiles to use, use her life magic on the forest tiles to recover health for your party. This will also generate more fire tiles, so like with Gale, try making large groups of fire tiles.
Ricard's strategy is the simplest: use fire magic.