Original is the only game type you can play. It is just the basic Game of Life. Along the way to completing all the miscellaneous achievements, you should earn at least three wins, if not more. The quickest and most painless way to grind wins is to play 2-player multiplayer (with you controlling both players). It does not matter which player wins, as long as you finish the game you will get a win added to your total. You do not even need to pay attention while grinding the wins. Just keep spinning the wheel and selecting random options for both players. Each game will take around 30 minutes if you are constantly spinning the wheel. I found this achievement best to boost while watching TV or something similar.
Make sure if you are playing pass-and-play multiplayer while working towards the miscellaneous achievements, that you finish the game if you are more than half way through to get credit for the victory.
NOTE: It would be a tad faster to play against the CPU since you can fast forward through their turns, but the game is still mostly luck-based and you may or may not win every game. If you lose to the CPU it will not count as a win. You could also use the "Home Button" trick to try to ensure victory, but this is likely more hassle than it is worth. Just stick to 2-player multiplayer and there is no effort involved.