Chu Chu Rocket has many different strategies to employ during the heat of battle, so I thought I would display a few that worked for me.
Some people say Offense is the best Defense. Start the match by stealing as many mice as possible. While that might seem like a no brainer, many players worry too much in the beginning about accidentally sucking in a Kapu Kapu with their aggressive play. Luckily, you'll have very few mice in the beginning rendering Cats nothing more than minor obsticles. Just ignore them until you amass a large enough lead over other players (Typically around 200 mice), and are long enough into the game (Usually under a minute) to use Defensive play.
Once you have a large enough lead, you'll find every other player targeting your poor little rocket. The bast strategy is to place arrows facing outwards from your rocket all around, as well as focusing on deflecting mice from your opponents rockets. Only switch back into Aggressive play once a Mouse Mania happens (Which means no Cats will spawn).
Method I've found to win me a couple matches. First, ammass yourself a lead in the game. Then, block off the hatches with arrows (Works best on matches with only a few hatches). This makes it almost imossible for your opponents to get a large ammount of mice.