Enlightened Fist has as a prerrequisite:
Spells or Spell-Like Abilities: Arcane caster level 3rd.
A Tiefling has Darkness as a spell-like ability with a caster level equal to its character level. Unless I'm reading the prerrequisite wrong, a 3rd level or higher Tiefling could acces the PrC as long as he accomplishes the other prerrequisites (quite easily being a Monk), however, the spellcasting class feature reads like this:
Spells per Day/Spells Known: Except at 1st level and 6th level, an enlightened fist gains new spells per day (and spells known, if applicable) as if she had also gained a level in an arcane spellcasting class to which she belonged before adding the prestige class level. She does not, however, gain any other benefit a character of that class would have gained (such as the bonus feat sometimes gained by a wizard). If she had more than one arcane spellcasting class before becoming an enlightened fist, she must decide to which class to add each level for the purpose of determining spells per day and spells known.
implying that he MUST have some levels in a caster class, and even if it didn't, a monk-only would have no list from where to draw spells, so... Can someone confirm if this is possible or not?