The battle shouldn't be too hard as the Ganymedis attacks aren't all that strong but you might have to heal at some points. Its only weakness is its head and it attacks with its pincers. Buff your members with whatever buffs they have and then attack the boss head on. When its health goes down a bit, it starts to jumps away and it will start firing missiles at you. These aren't that hard to dodge. When the bosses health gets to about halfway a cutscene will start.
After the cutscene you will be back fighting again. Use the same tactics you were using in the first half of the battle. This time feel free to use your strongest attack abilities in order to do some damage. Watch out for when it jumps away again because this time it will either shoot missiles or it will run at you, causing a lot of damage to any character it hits and a high chance of killing them. The plus-side of this fight is that the boss will only have half its health left. It shouldn't be overly hard to destroy the remainder of its health.