There are two ways to form a comparison degree of an adjective in Russian - they are called simple and complex forms.
Simple form is when an adjective itself is modified with a certain suffix:
красивый (positive) - красивее (comparative) - красивейший (superlative).
Complex form is when a certain particle is placed before an adjective, leaving it unmodified:
красивый (positive) - более красивый (comparative) - самый красивый (superlative).
Now the prefix наи- can be used either with the simple form of superlative degree to make it sound slightly stronger (although bit pompous) - наикрасивейший.
Or it can be used to modify a particle for a comparative degree to make it a particle for a superlative degree:
более красивый (comparative) - наиболее красивый (superlative)
менее красивый (comparative) - наименее красивый (superlative)
But it can't be used with simple forms of positive or comparative degrees (наикрасивый/наикрасивее is wrong) and it also can't be used with a simple form of superlative degree of an adjective that have negative prefix не- (I'm not sure that наинекрасивейший is grammatically wrong but it sounds weird).