In the Advaita Vedanta, Nirguna Brahman refers to a formless God without qualities and is the supreme. In Vishishtadvaita, it refers to God without negative qualities. However, I want to know what does Chaitanya Mahaprabhu's Achintya Bheda Abheda say about Nirguna Brahman?
Achintya Bhedabheda agrees with Visistadvaita on the meaning of the word Nirguna. Here's what this chapter of the Chaitanya Charitamrita says:
According to Vedānta philosophy, the Absolute Truth is a person. When the word ‘nirguṇa’ [‘without qualities’] is used, it is to be understood that the Lord has attributes that are totally spiritual.
It's also worth noting that Achintya Bhedabheda makes a distinction between Brahman, Paramatma, and Bhagavan. Here's what Srila Prabhupada says in this section of his commentary on the Bhagavad Gita:
The constitution of Brahman is immortality, imperishability, eternity and happiness. Brahman is the beginning of transcendental realization. Paramātmā, the Supersoul, is the middle, the second stage in transcendental realization, and the Supreme Personality of Godhead is the ultimate realization of the Absolute Truth. Therefore, both Paramātmā and the impersonal Brahman are within the Supreme Person. It is explained in the Seventh Chapter that material nature is the manifestation of the inferior energy of the Supreme Lord. The Lord impregnates the inferior, material nature with fragments of the superior nature, and that is the spiritual touch in the material nature. When a living entity conditioned by this material nature begins the cultivation of spiritual knowledge, he elevates himself from the position of material existence and gradually rises up to the Brahman conception of the Supreme. This attainment of the Brahman conception of life is the ﬁrst stage in self-realization. At this stage the Brahman-realized person is transcendental to the material position, but he is not actually perfect in Brahman realization. If he wants, he can continue to stay in the Brahman position and then gradually rise up to Paramātmā realization and then to the realization of the Supreme Personality of Godhead.
It is same as Vishistadviata.
Quoting from Laghu Bhagavatamrta of Rupa Goswami.
Brahma Tarka says:
"gunaih svarupa bh-utais tu guny asau harir isvarah na visnor nac a muktanam kvapi bhinno guno matah"
"The Lord is endowed with qualities which arise from his svarupa. The qualities of Visnu and liberated souls are not different from their svarupa"
Vishnu Purana says:(1.9.43)
sattvadayo na santise yatra ca prakrta gunah sa suddhah sarva suddheb-hyah puman adyah prasidatu
The material qualities such as sattva do not exist in the Lord. May the preeminent Lord who is purer than all pure beings be pleased with me.
In the same purana(6.5.79)
nana sakti bal-aisvarya virya tejamsy asesatah bhagavac cha-bda vac-yani vina heyair gunadibhih
The word bhagavan means that he is complete with knowledge, power, strength, opulence, heroism, and glory. He and is devoid of all inferior qualities.
Padma Purana says (6.227.39-40)
yo 'sau nirguna ity uktah sastresu j agad isvarahprakrtair heya samyukt-air gunair hmatvam ucyate"
In the scriptures, the Lord of the universe is said to be without qualities. This means that he is without inferior material qualities.
Bhagavata Purana says:
ete cānye ca bhagavan nityā yatra mahā-guṇāḥ prārthyā mahattvam icchadbhir na viyanti sma karhicit
The Lord possesses many other transcendental qualities which are eternally present and never separated from Him.
In Sanskrit rhetoric, there are two types of attributes: a quality or an action: dharmo guṇa-kriyā-rūpaḥ (Sāhitya-darpaṇa 10.48). A quality (guṇa) is the means of distinguishing something from something else in its category (jāti). Dr. Kāṇe expounds: “What is the distinction between jāti and guṇa? Jāti is never found disassociated from the individuals in which it resides, while a quality like śukla (white) serves to distinguish a thing from other things belonging to the same jāti.” This is Viśvanātha Kavirāja’s definition: guṇo viśeṣādhāna-hetuḥ siddho vastu-dharmaḥ śuklādayo hi gavādikaṁ sajātīyebhyaḥ kṛṣṇa-gavādibhyo vyāvartayanti, “A quality, the cause of the ascription of a particularity, is an established attribute of an entity. For example, the white color excludes a white cow from black cows, which are of the same jāti (genus, category)” (Sāhityadarpaṇa 2.4).
Brahman is unique, therefore it is not a jāti in the usual sense; rather, it is parā jāti, the transcendental category. Therefore, according to Sanskrit rhetoric Brahman cannot have a quality (a material quality). For instance, Akrūra says: anākhyeyābhidhānaṁ tvāṁ nato ’smi parameśvara. na yatra nātha vidyante nāma-jāty-ādi-kalpanāḥ, tad brahma paramaṁ nityam avikāri bhavān ajaḥ, “O master, O Supreme Lord, I bow to You, whose designations are unnameable. You, the birthless one, are Brahman, which is supreme, eternal, and unchanged, and in which hypotheses pertaining to name, category (jāti), and so forth do not exist” (Viṣṇu Purāṇa 5.18.52-53). However, Brahman has transcendental attributes.
satyaṁ jñānam anantaṁ brahma, “Brahman is real, is consciousness, and is infinite” (Taittirīya Upaniṣad 2.1), Śaṅkarācārya denies that Brahman has any kind of attribute and thinks Brahman is indirectly expressed.
Jiva Goswami quotes the explanation of Ramanujacharya from Sri bhasya 1.1.1 in his sarva samvadini commentary to Bhagavata Sandarbha. These are transcendental attributes of Brahman.