Catan

This might seem impossible at first, which is probably the reason that it is a gold trophy , but there is 1 way to do it, and ONLY 1 way.

The way to do this is to have 9 victory points and to NOT have the longest road. Then you have to build a settlement into the AI with the longest road, giving you 1 extra point for the settlement and 2 points for the 'Longest Road' for a total of 12 points. There are several things to consider here though.

The AI with the 'Longest Road' has to have at least 4 roads between his two houses/cities since there has to be two roads between each house/city. This is based on extreme luck as they usually have no more than 3 roads between their settlements. And the odd chance that they might have 4 roads between their settlements still means that you have to be close by.

Tip:
-Try and contest the AI for the 'Longest Road'. I have seen that if they are close to the 'Longest Road' they will prioritize to build roads instead of settlements. So you get ahead, let them catch up and as soon as they build some roads to pass you, hopefully you can build 1-2 roads and build a settlement in their road to claim victory.
-Be careful of the other AI's roads and not only the AI with the 'Longest Road'. I was so sure I had this trophy in one of my first games as my road was 7 and the AI's road was 9, I built one road (giving me 8) and a settlement into his 'Longest Road', only to find out that another AI had an 8 road as well. Thus giving me 10 points for the win as I shared the 'Longest Road' with the other AI.