The Marvel Comics' Celestials seem to be ridiculously hardy:
From Thaddeus' answer to Which Celestial's head is “Knowhere”?
From what we know of the Celestials in our Universe, (in the famed, Thor 3300) when confronted by the power of Odin, wearing the Destroyer, which was imbued with the power of all of Earth's Skyfather deities, and using the fire giant's Surtur's magical sword, Twilight, Odin was unable to harm even one Celestial for more than a moment. The indestructible Destroyer and Surtur's sword were destroyed seconds later. The power to sunder the head from a Celestial (and make it stick) must be incalculable. 
And from diras2010's answer to Which Celestial's head is “Knowhere”?
The Celestials are not indestructible, however. During the Third Host, the Celestials used their combined might to slay one of their brethren for breach of conduct.
And from Wikipedia
The characters are almost totally invulnerable, and have only been harmed in rare instances before instantly regenerating
So, what does it take to destroy a Celestial being?
Either from the Comics, or the MCU.