Energy can't be caught because it's not a physical thing. It's a measure of the amount of work something can do, how much impact on its surroundings something can have. And that something doesn't have to be matter. The energy of forces (their fields) can bend space-time to generate gravity just like mass does.

It's not a definition or anything, but I like to think of energy as the amount of "capacity to exist" in the universe.

As for the particle-wave duality... It's more a consequence of is thinking there IS a duality. Everything in the universe has "particle" properties like momentum or spin and everything can have wave behaviours like interference. Literally anything. Light has momentum. It can exert pressure. Even mechanical waves (sound) can have particle properties assigned to them (although they're called quasi-particles, because they're not real particles, like an electron). Particles can interfere.

In short, there's no such thing as a "pure" particle or wave, so there's not really any "duality". It's just that for certain interactions, particle-like properties are what we test for, while in others it's wavelike properties. But the point is that WE are selecting this.

It's like a cylinder. It can be a rectangle from one angle. It can be a circle from another. But it's not one OR the other. It's only the fault of how we choose to view it.