Mythos of Illuna

If an effect allows you to cast a spell without paying its mana cost, you can't choose to cast it and pay unless another rule or effect allows you to cast that spell for a cost. Similarly, you can't waive a cost reduction unless that effect says you may.

Any enters-the-battlefield abilities of the copied permanent will trigger when the token enters the battlefield. Any "As [this permanent] enters the battlefield" or "[This permanent] enters the battlefield with" abilities of the copied permanent will also work.

If the copied permanent is itself a token, the token created by Mythos of Illuna copies the original characteristics of that token as stated by the effect that created it.

If the copied permanent has {X} in its mana cost, X is 0.

If the target creature is an illegal target or if the token is no longer a creature when the token's granted ability tries to resolve, the ability doesn't resolve. If it's a legal target but the token is no longer on the battlefield when the ability resolves, the target creature won't deal or be dealt damage.

The abilities of the Mythos check what colors of mana were spent to cast the spell. It's not an alternative cost to cast the spell.