You are going to want to start a Dynasty with any 1 Star team (I choose Army). This way there will only be one year on your contract so you don't have to play/simulate through more seasons. Once you have chosen a team and started your dynasty, you're going to want to create a custom schedule. You only want to do this if you plan on simulating through the season.
Organize your schedule to make it the weakest you can by scheduling games with lower-ranked teams. After you are finished with that, simulate your season. By the end season you should have a decent enough record that the team will want to resign you to a longer contract. Continue simulating until you reach the screen where it asks you to sign another contract.
The achievement will unlock after signing the contract.