This was not too difficult, just make sure you have a Sim who has a little more time on their hands and can use that time to garden.
Gardens can/should be tended too every 24 hours. Make sure your Sim is happy enough and does not have many negative moodlets or is too hungry, tired, etc. Gardening adds nothing positive to any part of your Sims mood, and decreases Hygiene fast, always have them ready too bathe/shower after tending to the garden.
If you don't know how to begin gardening this is what to do. You will need at least 1 Garden skill before you can start gardening. You will have to take a Gardening Class at the Science Facility on the Town Map, go to the Library and read a book on Gardening Volume 1, or go to the Book Store and Purchase Gardening Volume 1. One you reach skill level one in gardening you can now watch the gardening station on the TV and increase your knowledge, and tending the garden will increase your gardening skill too.
You should by default already have some seeds, if not you can go to the Grocery Store and buy some, or look around different parts of town. On the grass in some areas you will see a small brown item on the ground, have your Sim pick it up, and you will have more seeds. (NOTE: Some rare seeds require you to be at a certain gardening skill level before planting.)
To place a seed and plant it you will need to go to Build/Buy mode, then press "X", go to Family Inventory. Under Family Inventory go to the appropriate area where the seeds are (the left panel). Choose the seed of your liking and place it anywhere outside on your property.
Now go back to "Live Mode" and have your Sim go plant the seed where you placed it. You will plant it and then click on it and "tend" it. NOTE: With a larger garden you only need to click Tend on one plant, and your Sim will fully take care of every plant.
Now here comes the part where improvements will begin happening. Take care of all your plants daily. Once they grow mature and start growing produce, you will start getting more to use. You can use the produce in your food and cut down on prices to prepare meals and it helps make better meals, or you can plant those pieces of produce too.
Once you have produce being collected from your plants, do the same thing as above in Build/Buy mode, once in family invetory you should have some produce with a better quality then what you planted. Plant those (feel free to sell your old ones for more money or space) and then keep tending those. Sometimes the quality will increase a little, but for the perfect plant you need to keep doing this. Once you have an outstanding plant, you should be able to harvest a perfect piece of produce from it. Plant that, and tend to it, once it matures you will have the achievement! You will also receive challenge points for each different perfect plant you grow!
Important Information:
Scale from Nice to Perfect:
Nice - Very Nice - Great - Excellent - Outstanding - Perfect
Fertilizing can help with making a plant be of and produce at a higher quality but is not necessary. And make sure never to fertilize with the death fish! Life fruit and garlic are the best fertilizers if you decide to fertilize.
Having the trait 'Green Thumb' helps but is not required. If your Sim does not have 'Green Thumb' you can always use use 'Lifetime Happiness Points' to buy 'Super Green Thumb' (which my Sim had) to greatly improve your gardening. To access Lifetime Happiness Points (obtained by completing wishes), press 'X' when in live mode, Use the bumpers to go to Sim Info, press right, and press "a" on Lifetime Happiness Rewards. My Sim had Super Green Thumb and was only at a skill level of 6 at gardening when I got my first perfect plant.
My first 2 perfect plants were Apple and Lettuce, they both grew extremely fast and increased high in quality quickly.