I consider trophy pokemon as pokemon that are difficult to get and as such classify them as competitive, shiny, and competitive shiny.
A competitive trophy is something with either flawless or near flawless IVs.
-Ex: my near flawless Latios with Hidden power fire.
A shiny trophy is a hard to get shiny Pokemon which usually requires lots of SRing.
-Ex: a legitimate shiny Mew/Latios
A competitive shiny combines the previous two definitions and is usually a product of dumb luck, RNGing, or MMing.
-Ex: a Flawless shiny Honedge with a quiet nature and the egg move wide guard.
I happen to have a few Pokemon from each category.
3DS FC: 4785-5475-7913. Friend safari: fire w/ Growlithe, Larvesta, and Fletchinder.
I'm getting my house fumigated so I won't be around for awhile... sigh.