Grow your pile of zombies into outer space.
You can complete this achievement by killing as many zombies as you can until your pile of dead zombies reach the outer space. Maybe, you are wondering, "Where is this pile??". You can find this pile in the Leaderboards option. The bottom of the pile is a garbage can full of dead zombies that you killed. This pile extends upwards until it reaches a black hole. However, you need not need to reach the black hole to complete the achievement, you just need to reach the outer space.
Here's what the pile looks like at the bottom.
The main strategy obviously is to KEEP KILLING ZOMBIES. However, there are certain Mini Games that gives you the chance to kill a great number of zombies. These are the following:
1. Last Stand
2. Column Like You See 'Em
3. Zombie Nimble Zombie Quick
4. I, Zombie Endless
5. Vase Breaker Endless
Just keep playing those levels and you'll reach the outer space.
And then later on, a planet.
I have yet to reach the black hole. :)
Good luck and enjoy!
See other related posts:
List of Plants Vs. Zombies Achievements