I like the two previous guides but if, you're like me and were after a quick achievement early on in the game to spur you on. This is the guide for you...
You'll want to be at the very first level of stage 2, the beginning of the night levels is the one to do it. You'll know its the one because you'll have just unlocked the puffshrooms and it will actively warn you against playing the level as its 'very difficult without them'.
Don't pick the puffshroom but pick sunflowers, cherry bombs, walnuts, chompers, mines and the 100 peashooters.
Essentially the issue here is sunshine and the key to gaining enough income is to sacrificing all your lawnmowers but one. Sounds daunting but easy. For most of the level all you will be using is the sunflowers and mines.
Pick your lane you want to build on and build your first sunflower. If its the first lane the zombies come down you'll want to restart. After that, continue to build along this lane until the lawnmowers go from the other lanes, using a mine well in advance if there happens to be a zombie on his way. Each time you've used a lawnmower start building sunflowers on that lane. Essentially you should be able to build up 10 sunflowers fairly easy if you're smart and then your income will be fine.
After building sunflowers you'll want to build one peashooter per lane and if it gets that point the level will essentially be over.
One final point, after a few sunflowers if you don't think the mine will arm in time put a walnut in front and concentrate on other lanes.
It sounds complex but it was both easy with some thought and satisfying to beat the game's warning. I completed this on 17/07/2012 having just started the game an hour before.