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There are a total of 16 heart containers in Phantom Hourglass. Many are gained via playing through the storyline bosses and through buying in shops, while others are only available through sidequests.

[edit] "Storyline" Heart Containers

1. After defeating Blaaz, Master of Fire in the Temple of Fire.
2. After defeating Cyclok, Stirr of Winds in the Temple of Wind.
3. After defeating Crayk, Bane of Courage in the Temple of Courage.
4. After defeating Diabolical Cubus Sisters in the Ghost Ship.
5. After defeating Dongorongo, Armored Lizard in the Goron Temple.
6. After defeating Gleeok, Two-Headed Dragon in the Temple of Ice.
7. After defeating Eox, Ancient Stone Soldier in the Mutoh's Temple.

[edit] Shops that sell Heart Containers

1. Beedle's Assistant sells a Heart Container when he is running the shop. You know that Beedle's Assistant is running the shop because the icon that shows Beedles ship sailing along the map screen is different from normal.
2. You can buy another Heart Container at any of the shops based upon islands after you've gotten the bombchus and gotten the bomchu bag from the shop upon Goron Island.

[edit] Mini-Games Whose Prize is a Heart Container

1. The fishing minigame, which becomes available by finding the mermaid of Molida Island after speaking to the Old Wayfarer. The Old Wayfarer will give you the fishing rod after he lands the 'mermaid' into his indoor pool. You have to fish a lot before you get the opportunity to catch Neptoona, the ultimate fish.
2. The Traveler's Ship. Defeat the crazy old guy trying to be a hero by managing to hit him 100 times or more before he can hit Link three times.
3. Getting 2000 points or more in Romano's archery game upon Molida Island.
4. Complete all three levels on Maze Island.