I thought we had a topic for this but I could not find it, so here is a list of the Permanent Quests that include the reward for each one as well as if there is a dragon requirement.
As a note if the requirement lists a rarity that means that that is the minimum rarity required. For example, if it requires a Very Rare, then you can use a Very Rare, Epic, Legend or Heroic to meet that requirement.
Tournaments/Quests
[Reward] (dragon Requirement) if no dragon is listed as the reward, the reward is the namesake of the quest.
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Beginner's Cup [Aztec]
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Martial Arts
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Origami (Electric)
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Prehistoric [Pterodactyl] (Electric)
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Frozen Wind (Ice)
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Giant [Giant Wings]
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Amethyst (Metal)
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Black Knight (Dark)
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Twister (Archangel)
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Lava
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Bad Box [Box]
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Twin
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Planetary [Saturn] (War)
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Genius [Genie] (Pure)
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Asgard [Loki] (Legacy) Legacy is very difficult to breed, use two legend only element dragons
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Albino
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Sunset (Nature) (Flame)
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Sky Queen (Flaming Rock)
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Boreal
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Kaiju
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Obscure Finale [Obscure]
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Molluck
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Dragotron (Kratus)
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Felidae (Legacy)
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Rockfire (Felidae/Immortal) Immortal is difficult to obtain, buy when it is on sale, or try to breed when it is on the breeding island
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Infamous (Rockfire/Drathic) use one element dragons to breed for Drathic, using Legend and Beauty
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Delicate
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Petrified
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Magician
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Two-colored
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Blossom
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Hi-Tech
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Acrylic
Note: If I missed any requirements, please let me know.
Note 2: If you are missing a required dragon, you could also try to see if it is available to be rescued rather than buy or breed it. Keep in mind for the rescue you must complete all rarities lower than the rarity you are attempting. For example to rescue a Legend dragon all prior rarities must be fully completed at least once each.