"Nebulaphile," although not a real word, is related to the word "nebulaphobia" which is the fear of fog. The word "phile" means to love or like something, so the word "nebulaphile" means to love or like fog.
To get the achievement successfully, you should pick the following:
Scaredy-shrooms play the most important role. They are cheap and let you know if there are any zombies in a lane. As the achievement states, you cannot use the fog removers. Gloom-shrooms are cheaper than Threepeaters, so they should be used. A good strategy is to plant Garlic with Tall-nuts and Gloom-shrooms behind them on the second and fifth lanes.