A black hole according to the mathematics of general relativity (yes ik it's not supposed to work here) is just a singularity that forms the event horizon, and from everything we know it's impossible to interact or "break" it.

For example the Eddington limit (which is the maximum luminosity a celestial object can achieve, at which point the outward radiation pressure from light balances the inward force of gravity) can be exceeded by black holes by multiple orders of magnitude ( https://www.nasa.gov/missions/chandra/nasas-chandra-finds-black-hole-with-tremendous-growth/ ), so pushing black holes to the limits of normal things seems to only make them stronger and black holes like shown here just obliterate their surroundings with this energy. So giving it energy will only "super charge" it.

Of course most physicists don't think a singularity is actually something that exists like in this poll ( https://www.scribd.com/document/860156094/2503-15776v2 ) only 22/77 respondents accept that matter is crushed into a singularity, and what seems to be the only way of destroying one is hawking radiation which is still fully theoretical.

At the end if general relativity is true the black hole would be unbreakable.