The card types that could appear among your permanents and cards in your graveyard are artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Supertypes, such as legendary and basic, aren't card types.

The second triggered ability of Happily Ever After has one very long intervening "if" clause. This means that all of the conditions must be true as your upkeep begins—you must control permanents with all five colors, your permanents and graveyard must contain six or more card types, and your life total must be high enough—or the ability won't trigger at all. If they're not all true as the ability resolves, you won't win the game.

Players can't take any actions during your turn before your upkeep begins.

Lands are normally colorless permanents, even if they tap for mana of a certain color.

You could have one permanent that's all five colors, or the five colors could be spread out among any number of permanents.

In a Two-Headed Giant game, Happily Ever After's first ability causes each team to gain 5 life twice.

Ignore the alternative characteristics of an adventurer card in your graveyard. Its alternative card type won't be counted among the card types of cards in your graveyard.