In normal mode, the player has to beat the zombies at level 1.
Difficulty
The combination of Zombie Fighter and Double-Cabin Aircraft Zombie is a deadly one. Both zombies can do considerable amount of damage to your ship. As this is a Special Delivery level, you are limited to only a few plants. Aspiragus is your only offensive flying plant, so they should be planted at the 4th column. The player must also be wary of the thunderbolts that will strike on plants as it can give plants unfavorable conditions.
Strategies
Thunderbolts are fairly easy to deal with on the first three columns. Ampthuriums can easily remove the status from the plant before it gets stunned, gets damaged continuously, or gets slowed down.
Shovel up plants on the sky that are affected by thunderbolts, as Ampthurium can only remove statuses from it on the tiles surrounding it.
Use Plant Food on Aspiragus to take down multiple zombies, especially to zombies like Zombie Fighter.
Difficulty
In hard mode, Zombie Fighter and Double-Cabin Aircraft Zombie pose more of a threat than in normal mode. Thankfully you are given Aspiragus, a plant you can upgrade via stars, but that alone is not enough for taking out multiple zombies that absorb huge amounts of damage. Other plants should be upgraded to ease up the level.
Strategies
Do as what you did in normal mode, but with leveled-up plants and zombies.
The small number next to the zombie icon means that zombie will always appear in that lane, with 1 being the topmost lane and 5 being the bottommost lane.