Rewards are based on your overall stats at the end of your adventure. The highest stat rarns you the first place reward, the second highest earns you the second place reward, and so on. If two or more stats are equal, you can choose which of those stats count as the highest and lowest. Challenge Rewards and Smugh Rewards are earned so long as you meet their criteria, regardless of stats.

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Love
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Frilly Garb for having fourth place love.
Swimsuits for having third place love.
White Gown for having second place love.
Bunnysuits for having first place love.

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Lust
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Nun Guise for having fourth place lust.
Sweater for having third place lust.
Lingerie for having second place lust.
Dom Attire for having first place lust.

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Wealth
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Slave Gear for having fourth place wealth.
Barmaid Duds for having third place wealth.
Party Dress for having second place wealth.
Maid Kit for having first place wealth.

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Power
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Idol Costume for having fourth place power.
??? for having third place power.
Battle Suit for having second place power.
Knight Armor for having first place power.

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Challenge
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Refresh, allowing undead to look "alive", by saving all undead princesses.
Dullahan Princess, reuniting Crest Princess and Armor Princess into one being that shares aspects of both.
Primordial Princess, the combination of Dullahan Princess, Arcane Princess, and Sword Princess, that encompasses all of their strengths and weaknesses.
Dragon Queen, the mother of the Grand Tower Kingdom, allies with you if you convince her five daughters to join you.

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Smugh
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Alt Costumes, for having (x amount) ways of transforming characters' appearance.
Palette Swaps, for having (x amount) of the same color prncess.
Become Smugh by saving absolutely nobody. Congratulations...?
Tower Princess, by finding a way to save absolutely everyone.
Angry Letters for skipping a non-expansion gen. You can rescue two more individuals from one gen per skipped gen.
Grand Banner for rescuing four or more factionless companions, allowing you to rule over a council that oversees the continent.
Champ's Belt for only rescuing princesses that follow a similar theme. Anything that is of that theme is yours to control.
Mystery Box for forfeiting all rewards you were elligible for. What's in the box?