Call recording

Yes, the recordings made by X would be considered illegal as they are made without Y’s consent and were posted online in order to damage the reputation of the company. As the phone tapping is considered unlawful if done by third party and not by the government in special cases.
Section 5 of Indian telegraph act, 1885 states that no individual has the right to intercept communication of another individual, only the Government of India has the power to take position of any license telegraphs in case of public emergency or in interest of public safety. 
In the landmark case of People's union for civil liberties (PUCL) v. union of India (1997) 1 SCC 301 AIR 1997 SC 568. The Supreme Court stated that the right to hold telephonic conversation in the privacy of one’s Home or Office without interference can be claimed as ‘right to privacy’ and a telephonic conversation is a vital aspect Mans private life. The court also ruled that telephonic tapping would be violative of article 21 of the constitution unless it was permitted by procedures established by law and it would also be violative of right to freedom of speech and expression under article 19. 
However, under Section 5 (1) and (2) of the telegraph act, state and central governments are allowed to tap phones after approval from designated authorities.
In the case of Rayala M. Bhuvaneswari vs Nagaphanender Rayala AIR 2008 AP 98 the respected High Court of Andhra Pradesh held that, the act of tapping itself by the husband of the conversation of his wife with others was illegal and it violated the right of privacy of the wife. In this case the husband was taping the conversations of his wife. The consent of the parties to the conversation was not there.  
Taping of telephonic conversation is illegal by any third party in India. It is only allowed to the government on the basis of specific laws and rules and after following the procedure specified as per the relevant laws. Due to the privacy worries, even if someone permits or consents to their telephone being taped and conversations being recorded, it remains illegal as the second party to the conversation has still not consented to tape.
Remedies against phone tapping
1.    The aggrieved party can file a complaint with the National Human Rights Commission (NHRC).
2.    The aggrieved party can also file an FIR against unauthorized tapping.
3.    The aggrieved person can also move to the Court against the person doing any unauthorized act under Section 26 (b) of the Indian Telegraphic Act.