Particle energy = Planck's constant x wavelength. You want a simpler explanation, but that is as simple an explanation as there is, a single equation relating two variables by one constant. It is an observed fact, and a whole lot simpler than an apple falling on your head due to the hypothesized force of gravity.
Your problem is that you confound every day experience with simple. But, unless you squint your eyes and observe the diffraction through the slits of your eyes, wave-particle duality is not a part of your daily experience. In a laboratory it could be. Most everyday phenomenon are, in fact, far more complex. Wave particle duality only doesn't matter in those cases where there are so many waves interfering with each other that that wave interference effects all wash out and all you see is the gross features of the classical everyday world.
It is not wave particle duality that science has a hard time with, but trying to explain classical physics and the lack of time reversal asymmetry associated with the tangible world.
Yes, the erratic time-dilation effect messes up every observation from any angle every single time.