The achievement's name is a reference to the 1948 film "I Walk Alone."
The best way to earn this achievement is to replay The Boonies Level 1. Plant one Peashooter where it can hit the zombies easily without being attacked too soon. With sufficient luck and clever use of Gardening Glove or Lawn Mower, it is also possible to achieve this in other levels in The Boonies. If not possible, wait until other plants and VIP plants are unlocked to easily earn this. On later levels, this achievement would be impossible to get due to the huge amount of zombies spawning.