PS4 trophies made an excellent video listing all the plants and it's locations; just remember that you need to plant each seed you find to make them grow. After all of them are full grown, you'll get the achievement.
Edit 2: As more people have unlocked the achievement (on Xbox and other platforms), it's been clear that the only requirement to make the seeds grow is time, either leaving the game running without doing anything or just traveling through the different planets, killing enemies and/or trying to unlock other achievements.
For the people who are still doing the main missions, here's the time stamp from the "Ideal" order to gather all the seeds:
1:28 Royal Fluzz
6:09 Milk Grass
7:32 Bleeding Cut
For those who already completed the missions, the order to gather the seeds is not important, but the timestamps can help you identify which plants are missing on your terrarium (that's the actual order they're planted in the game, even if you missed some of them in your first try).
Edit: as some players commented, the distance between the player and the ship, while a plant is left "growing", may be a factor for it to grow faster. It doesn't matter if it's while playing the regular story or post-story while trying to get other achievements (which was my case). I made grow at least 4 plants while traveling to Zeffo and Bogano, moving a little far from the ship, kill some troopers and going back to the ship to check (for me, Bogano has the least "complicated" route to return to the ship if you stray to far from it).