Catan
12 Achievements
200
15-20h
Builder of Catan
You won Longest Road 10 times.
20
How to unlock the Builder of Catan achievement in Catan - Definitive Guide
So I suggest this setup :
1 player mode with 3 Easy AI.
7 victory points
Quick game (to get the second settlement upgraded to a city).
You should use the option to fix who starts the game and take seat 4, this way you are the first to place your city. Try to get wood and brick so you're able to immediately build two roads. The Easy AI will pretty much never keeps you from trading a card for another, so it should be easy to go for the third road , giving you the card (make sure your two first roads that come free before the start of the game can be connected) on your first turn.
At that point, you have 5 victory points and just need to end the game asap. Just build two more settlements, or one settlement and a city. By abusing trading two-for-one with the AI you'll just need one or two turn.
4 AI
10 Victory Points - Standard Game
To get the Longest Road card, you need to build at least 5 roads that touch one another. To keep the Longest Road card, you must have more continuous road than any other player in the game.
After 10 games of doing this, you should get the achievement.
TIP: Do NOT do this achievement along with Citizen and Knight of Catan. If you are to get all 3 achievements, or any other achievements, simultaneously in this game, it will record one and void all the others unless you load Catan onto another Xbox 360 and recover your gamertag. This is the only known workaround. View Xebu's comment below for more information.
You must win the 'Longest Road' award 10 times in matches. This will most likely unlock whilst you collect VP for other achievements but it does not take much effort to unlock. The longest road award is given to the player with the longest single road on the map that is over 5 sections long. There are two ways to get this, either gather lots of wood and brick cards or hope you are lucky with development cards and get road building twice. The first method is probably easier and you will probably be doing this anyway to win matches.
When you start a match, position your first settlements in spots that will gain you wood and brick cards then wait until you have enough resources for a road and add it on to one of your settlements. Be sure that you have one long road and not a branching road or it will not count. Win ten matches with the award and you are done.
You can check how long your road is by pulling the right trigger, the number next to the road icon is the number of road sections you have in your longest chain.