The only Trophy Shop exclusives are the Character Alternate Trophies which will start to appear in the shop after you clear Classic with the chosen fighter. (Wii U Only)
Example: Clearing Classic with Sheik on Wii U will unlock the Trophy in te Trophy Shop, if you keep checking, the trophy will appear eventually.
If you are looking for Final Smash Trophies, you get those from clearing All-Star Mode. (Wii U Only)
The only other trophies that are exclusive to a specific game mode are the Trophy Rush Exclusives, trophies that you can only find in the Trophy Rush game mode.