Could God create a rock so heavy...
One of the challenges we face in Worldbuilding is when we deal with absolutes. You have a rock that is unbreakable. The Juggernaut can't be stopped once he starts moving. Aliens bring us a source of unlimited energy. These ultimate extremes are appealing because they appear to bring excitement to the universe which doesn't exist in the real world.
Unfortunately, we often find that our ultimate creation is too ultimate, and we need to create something that can defeat it. The only problem is that you've already woven a ton of handwavium style arguments into your creation. You're not satisfied with any easy solution. Your awesome creation has become your biggest pain in the rear!
The first step is to remember that this is your handwavium, by your rules. You can change your rules. You say:
It's a rock that exists in two alternate universes, and always interact with each other, therefore making it virtually indestructible, only by destroying both at the exact same time.
You've intentionally created something that, by that exact wording, cannot be destroyed within one universe. That was your wording. You penned it, you chose to live by it. It shapes your world, and ironically becomes as unbreakable as your duouniversal shield itself.
You can choose to change that rule, so that there is a way to destroy it, or you have to only focus on solutions that work in both universes. This is basic logic. It's hard to compete with logic when you were the one who wrote the assumptions.
We're going to have to look at how connected the two universes are. If there's no communication between the two universes, so it would be impossible to coordinate an effort to break the shield on both sides, then you have written yourself into a corner, and you can sit in it. Your duouniversal rock is now stronger than the entirety of the rest of both universes combined. How can you fit that into your story? Can you make it a focal point?
Perhaps we can allow more communication between the universe. After all, we have a rock that's in both universes, why not other things? Perhaps we could have something which exists in both universes and causes something to vibrate in opposite directions in the two universes. Symmetrical devices like that are always interesting. You might be able to use it to cause one rock to vibrate one direction, one rock to vibrate the other, and in the regions where the rock is no longer overlapping in both dimensions, chip away at it like normal rock.
In the end, its up to you to invent handwavium to combat your own handwavium when it gets you into trouble. There is no one answer: there is at least one answer for every ruleset you consider for resolving your handwavium troubles. Go explore, and find what is best for you!