Story Related. This will unlock after chasing down Einstein and giving him a hotdog sample to earn his trust.
Once you have learned about all of the illegal things in Hill Valley from Biff, you need to find a way to get a dog. Go over to the soup shop and read the sign that says "Free Samples". Open the window and ask for some free samples. Now try and walk into the back alley and you should see Einstein hop over the plank into the back of the area. Walk over to the plank and climb over. Examine the fridge, and Einstein will escape. Now pick up the spray can near Jennifer, and use it on the plank. Leave the back alley and then enter again. Walk back over to the newly painted plank and climb over. Now you should see footprints showing where Einstein is hiding. Interact with the table to discover Einstein. Give him your hotdog sample to earn his trust, then let the scene play out. This will result in you getting demerits, and a new trophy.
Refer to "Final Solution" for the trophy walkthrough.