What are the attainments not to be claimed by a monk?

I trust Bhante @Brahmali would be the best one to dive deep into these definitions. Further below this passage you have some other interesting definitions and an extensive list of all permutations and their respective offenses. There you may have a preliminary answer to your question:

##Definitions (for the permutations)

Absorption: the first absorption, the second absorption, the third absorption, the fourth absorption.

Release: emptiness release, signless release, desireless release.

Stillness: emptiness stillness, signless stillness, desireless stillness.

Attainment: emptiness attainment, signless attainment, desireless attainment.

Knowledge and vision: the three true insights.

Development of the path: the four applications of mindfulness, the four right efforts, the four bases of supernormal power, the five spiritual faculties, the five spiritual powers, the seven factors of awakening, the noble eightfold path.

Realization of the fruits: realization of the fruit of stream-entry, realization of the fruit of once-returning, realization of the fruit of non-returning, realization of perfection.

Abandoning the defilements: the abandoning of sensual desire, the abandoning of ill-will, the abandoning of confusion.

A mind without hindrances: a mind without sensual desire, a mind without ill-will, a mind without confusion.

Delighting in empty dwellings: because of the first absorption, there is delight in empty dwellings; because of the second absorption, there is delight in empty dwellings; because of the third absorption, there is delight in empty dwellings; because of the fourth absorption, there is delight in empty dwellings.

This last bit could be what you are after.

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