Perfect games are games in Head Soccer in which you score at least 10 goals and don't allow your opponent to score any. The reason these are called perfect games is because if you do this it completes two Achievements: win by at least ten goals, and win without allowing a goal.
Perfect games have no real purpose other than to unlock two hard achievements against the same person with only playing one game. But getting a perfect game also brings a sense of pride as not just anyone can get perfect games.
There is no real strategy to perfect games, except use your best player, and do your best. These are hard to do, but it is really cool if you can get a perfect game. The best way to get lots of goals is using headers. This is a trick to jump to the ball after the ball appear on the middle of the field and you will use your head to make an goal. This way you can get a lot goals. You can also use a good Costume, such as Uruguay's Costume. Use it on your opponent, push him in his own goal and kick the ball also in the goal.
In Arcade, a perfect game is what I described above, but there are different versions of perfect games for each game mode. A Perfect Tournament is when you score at least 30 total goals and don't allow a single goal. A Perfect Survival is when you make it to at least level 49 before allowing a single goal. And a Perfect League is when you finish 18-0, each game having been a Shut-Out. A perfect Head Cup is when you make more as 50 goals and not much goals get back from your opponent. A perfect Death Mode is when you get more as 70 goals and not many goals from your opponents. This is almost impossible, since there are Obstacles in Death Mode.