There are 5 different kinds of tails in the game, excepting the rat tail. Certain monsters drop them - Green Dragons drop green tails, Yellow Dragons drop yellow tails, Armored Fiends drop black tails, Flan Princesses drop pink tails, and Red Dragons drop red tails, all of which you can use to exchange for the Adamant Armor (pink tail), or Onion equipment which grows stronger depending on your level. I only was able to get a green tail after about 100 battles with a Green Dragon and a black tail after ~20 battles with Armored Fiends. The Siren item used in certain places is necessary to get into battles with some of these enemies, and the only way to battle them with consistency.