Persona 3 Reload

On 5/25, the director will ask you to go to the dorm rooftop during the evening. He will explain the garden and give you a seedling. You can plant the seedling there and harvest it on 6/4.

To get the achievement, you have to wait until 6/16 after Fuuka moves in. You can spend time with your dorm mates at night and one of the activities is gardening. On 6/16 Fuuka will want to garden with you. If you use tomatoes you can get this achievement on 6/26. Harvest that crop and you will get this achievement

Port Island Station flower shop also sells seedlings if you didn't want what the director offered

How to unlock Eat Your Veggies, Peas!
On June 16th, Mitsuru will give you a tour of the dormitory… which seems rather redundant, considering you’ve been living there for more than a few months by this point. However, it’s anything but redundant!

It’s here where you’ll learn a few more things that you can do to spend your evenings wisely, like cooking, reading, watching DVDs and gardening with teammates. Perhaps the best of them all, is that you can garden with teammates, and when you do, it boosts the productivity of your veggie garden.

For instance, if you buy the Soul Spinach Sprouts from Rafflesia for 1,200 yen and plant them on your own, you’ll get 3 items that restore 30 SP to 1 ally (really helpful items if you want to do a block of Tartarus in one sitting), but if you do them with Aigis and/or Fuuka as well, you’ll get a bumper crop.

On top of your original batch, if you do it with Aigis, you get 2 x Leafy Soul Spinach, which restores 30 SP to all allies; and if you do it with Fuuka, you get 2 x Large Soul Spinach, which restores 50 SP to 1 ally. If you do it with both, you get the lot!

So, when you see an opportunity to speak to Fuuka or Aigis at the bottom of the stairs, and have already planted some crops, then agree to let them help. Not only will you get a bumper harvest, but you’ll also get the ‘Eat Your Veggies, Peas!’ chievo too.