Arete retreats after you defeat her in the forest, so you follow and have to fight on floating islands.
Before the Battle
Be sure to bring a unit that knows Locktouch, because there are several treasure chests in this map, but no chest keys at all.
Arete is in the northwest corner of the map, and you start in the southeast. To reach her, you will have to use the floating blocks throughout the map. These blocks will move from their positions at the end of the enemy phase. The blocks always stop at a location with a "dock" made of stone that looks like the floating blocks themselves. If you put some non-flying units on one of these docks, a floating block will eventually come to them.
Any unit that is on a floating block at the end of the enemy phase, whether friend or foe, flying or non-flying, will be moved along with the floating block.
There are some treasure chests along the west side of the map that contain some pretty rare treasures, so be sure to bring a Locktouch unit to access them, since there are no chest keys to be found in this map.
Several enemy units will also drop items when defeated, so be sure to look for those, since the dropped items are also pretty rare.
From the island where you start, there is one floating block that you can reach. It can go between your starting island and the central island.
From the central island, there are a few stone docks. One is on the south end of the central island, and the floating block that stops there will go to the southwest part of the map. Another stone dock is in the northwest part of the central island, and the block that stops there will go to the west part of the map. Another stone dock is in the northeast corner, and it goes between the central island and the northeast part of the map.
The only way to reach Arete is to use that northeast dock from the central island. The other docks from the central island only take you to the treasures on the west side of the map.
After you are done collecting treasure and dealing with enemies in the southern part of the map, your non-flying units will need to go to that northeastern dock from the central island and walk onto the floating block when it arrives there. After that, you will be in the north part of the map, where you can make your way west. There is another floating block that only leads to a small island with two forts on it. You can always put your units onto a fort to heal up, since the forts also function as heal tiles. Otherwise, when you are ready to end the battle, continue to the northwest part of the map and defeat Arete to use the seize tile that she was standing on.