I recommend using Costa Rica for this achievement as the team is well balanced (most players have an overall rate of 75 or something like that).
I had tried to advance past the Group Stage using Togo but the players are not good (apart from Adebayor).
Try to play 3 or 4 star teams. Most people will choose 5 star teams (Germany, Spain, Brazil, Argentina, etc) so you will need a bit of luck - just be aware you CAN quit on the very 1st screen (when you find out which team your opponent has chosen). Go back to main menu and search again.
There are bad players out there using 5 star teams so if you're good you will qualify. I managed to beat Argentina, Germany and Spain but the players were not very good. Well... good luck!