At the start of Act 2, in the basement, pick up the orange flowers on the workbench and put them in the big green machine next to the beehive. That's one.
Later in Act 2, in the town square, look at the two pots of flowers in the window above the newsstand. The yellow potted flowers will be lowered down after a short cutscene and you can take them. Later we'll take them back and feed them into the machine too. That's two.
Talk to the lady at the newsstand and she will ask for words. She'll ask for different words in a different order each time. She's trying to craft an insult, but it turns out what really insults the man upstairs is being called a "mild gentleman."
For the first two or three words (it seems to vary depending on how many times you go through the scene), what she asks for varies, but it doesn't matter what you pick.
When she says she wants a DESCRIPTIVE word, select "Mouth Melters - Mild."
When she says she wants a PERSON, select "Stuff for Gentlemen."
Once properly insulted, the man upstairs knocks the purple potted plant down. Pick it up and take it back to the basement. Feed both potted plants into the machine. That's three.
(You actually need the potted purple pansies to finish the act, but if you feed them into the machine then return to the town square, they will have reappeared. You won't have to run through the insult game again, either.)
At the end of Act 2, as part of the story, you will create giant daisies using the growth formula. When you feed this fourth flower into the machine, the achievement will unlock.