By the flat triangle mesh I basically mean a square consisting of a few triangles (thus the shards).
From a theoretical perspective you'd basically start rendering the 3D scene normally, then when it's time for the effect you'd save the current frame, clear the screen, load the mesh and size it up to the view frustum (to fill the screen), project the saved frame onto the mesh, then trigger your "shatter" animation.
In terms of implementing this in DBPro, well... I haven't touched it in a long while so I wouldn't be able to tell you what commands to use. You should be able to make the mesh animation in something like Blender, then program the rest in DB. Unfortunately DBPro's a rather high level language (to admit entry level programming), so it might be a bit difficult to implement some of this. I suppose that's why I try to use more low level APIs such as OpenGL or DirectX for graphics programming.