There are very few Side Quests in Final Fantasy IV when compared to most other Final Fantasy games. We have outlined the available quests below.
– Creating the Excalibur Sword from the Legend which was found on Mt. Ordeals
– Creating the Adamant Armor, which is acquired from the bizarrely titled Pink Puff’s tail, located in the Moon’s Core, and Adamant in the Underworld.
– Getting the Summons Leviathan and Asura from the Land of the Summoned Monsters.
– Finding the injured Yang in the Sylvan Cave will allow Rydia to summon the Sylph summon. Additionally, striking Yang with his wife’s Frying Pan will earn you the Spoon dagger / knife, which is certainly worth having.
– Obtaining the summons Odin and Bahamut.
– Gaining the item-based summon spells of Imp, Bomb, Cockatrice, and Mage. These can be acheived by killing the aforementioned monsters until the items are randomly dropped.