Which adjectives can describe 'intellect' and 'education'?

you could say "higher intellect and superior education." Your sentence could look like this: In order to acquire this, one does not need a superior intellect, nor higher education.

One strategy for adding originality to your adjective selection is to choose one that pertains to the quality that you're evoking. Great can attach to so many nouns and noun phrases. More verbose versions of great (like excellent) are more emphatic but no more specific. However, a word like sagacious pertains specifically to discernment:

2.a. Gifted with acuteness of mental discernment; having special aptitude for the discovery of truth; penetrating and judicious in the estimation of character and motives, and in the devising of means for the accomplishment of ends; shrewd. (OED)

So someone who has a sagacious intellect is shrewd and can likely plan out a large project. They are not likely to be fooled by appearances.

Whether that word works or not, you can use a search strategy of going between synonyms and near-synonyms in a thesaurus, seeking adjectives specific to mental faculties, in order to find the precise emphasis you want.

"brilliant" seems like a good fit.
(one does not need a brilliant education)

• outstanding, exceptional, splendid, magnificent: having or showing unusual and impressive intelligence: a brilliant mind; a brilliant solution to the problem.

. Bertrand Russell had a brilliant mind.

. Mozart showed his brilliance at an early age.

. To leave half and hour earlier was a brilliant idea.

. "the defective moral training of many persons in the upper classes who have had a brilliant education".¹

. "From 1833 to 1840 she received a brilliant education according to the ideas of the bourgeoisie." ²

Consider incisive for intellect and extensive for education, as in:

... one does not need an incisive intellect, nor an extensive education

I personally like these choices for their alliteration. Examples of their usage in the wild below:

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He embarked on a 90-minute discourse that showcased his incisive intellect, his rambling imagination, and his almost pathological attention to detail.
_{LA Times}

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Even to work in museum as a guide requires extensive education and training.
_{NY Times}

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