Note how a lot of instant kills are designed to be under "required plants." This is because they can easily be used against the Zomboni.
Plant Sunflowers and Potato Mines in the beginning of the level to kill the first few zombies and obtain more expensive plants. Start planting Repeaters preferably when the first Conehead Zombie arrives.
When a Zomboni comes, use a Jalapeno to kill it and its ice trail. If you don't have enough sun, plant a Squash to kill the Zomboni. However, it will not take away the ice trail.
If you wait for 30 seconds, the ice trail will go away.
Make sure that you plant two columns of Sunflower because Chompers cost much. Once two columns of Chomper are planted, you can easily beat groups of zombies, including Zombonis. Remember to keep planting Chompers.
Before planting a column of Chompers, you can use Potato Mines to defeat the first zombies until you have enough sun to plant five Chompers.