Is it correct to use "balances of nature" plural form, for natural equilibriums or are there some other ways to say the same thing in plural form?
Balances of nature is indeed the proper way to pluralize the term.
Knowledge is so imperfect about the balances of nature, and these balances so fundamental to the existence and the perpetuation of life, that they should not be tampered with, even if the risk involved is small. (The Wisconsin Seminar on Natural Resource Policies in Relation to Economic Development and International Cooperation, Vol. 1)
It is more common to speak of "the balance of nature" then "the balances of nature".
The singular describes the idea that nature is in a stable state meaning that changes to part of nature will affect other parts.
The plural emphasizes the plurality, i.e. there are multiple things being balanced.
After seeing your context, I would personally use an alternative that will let you keep the "<adjective> <noun>" pattern.
Fragile Ecosystems... (common phrase)
Delicate Balances... (common phrase, audience will infer "natural" from the image displayed)