Use Aether attacks and your champions' Aether attacks for maximum damage. Each time a character gets killed, the ship will lose an amount of health equal to that character's maximum hit points. This will happens for both spawned characters and for new characters. Focus on attacking the easiest enemy to quickly destroy the enemy ship. To do the maximum damage possible, use Aether and champions' Aether attacks. Stand on the Aether platforms in the middle of a battle to charge your Aether faster, and earn Aether each time you get hit.
Purchase more party members to be able to bring more champions with you in battle and strategize your team more effectively. You can also purchase more shells to have more ways to damage enemies and other ships.
Purchase new ships based on what kind of defensive strategy you are planning. For example, if you purchase the Arc, it will not take damage in the center and will allow you to concentrate your defense on both of the sides. On the other hand, the Sparrow is only vulnerable in the two middle lanes of the ship.