A very difficult achievement indeed, you will need to be either very lucky or very strategic. You must beat three hard AI players in a match, you may end up playing a lot of matches and losing before unlocking this achievement. Here are a few things to remember if you hope to win.

Collect development cards. There are five VP cards in the deck, getting those helps a lot. Road building cards will be important for getting the longest road award and the two VP it holds. Soldier cards are an easy way to gain resources and will hamper the other players' advancement, you can also get two VP for the largest army award.

Positioning settlements. Be sure to pick good spots for your first settlements, allow yourself room to move about the map and settle on other tiles. Make good use of the ports around the edge of the map, using the to reduce port trading costs will help out if you are short on resources.

Trading. Hard AI will rarely trade with you, so never assume you can progress after some friendly trading. However, you will come across the rare opportunity to trade so make sure to seize the moment. Port trading will be a much better option so try to settle on or near ports that favour the resources you gain a lot of.

Don't be afraid to quit a match if things look hopeless, there is no point in wasting time when you are destined to lose, so long as you don't take this mentality into online matches =P