The I, Zombie minigame is the first of the Minigames of I, Zombie. Although the first one is quite easy, lack of knowledge about DPS and Zombie's health have resulted in many fails.
As you start with 150 sun, it would be unwise to spend 125 on a buckethead right away. Instead:
1. Send out a Zombie (50 sun) into a row with only 1 Peashooter and is directly 2~ spaces behind the red line. Do not worry about a Squash killing your Zombie. Use another Zombie to take the rest of the row out.
2. After you gained an amount of Sun, use a Bucket head to clear down a row. Do not worry about a Squash killing it, unless there is a Peashooter directly behind it.
3. Following 2, if a Peashooter was behind the late Squash, send another Buckethead down. If not, a normal Zombie will do.
4. You should have lots of Sun by now. Either repeat 1, 2, and 3 or use Football Zombies to clear Squash-less rows. Use the Zombie for a buffer.
5. If you haven't done it in 4, use the Football Zombies to mow down everything else.