The following information is taken from the Steam Achievement guide but Steam user "Aru" here https://steamcommunity.com/sharedfiles/filedetails/?id=14294...
who has lovingly crafted the guide for achievements in English and German.
"Get 5 stars in the category "Equipment" of the Garden Contest. You can enter the Garden Contest by pressing Enter (sell the house) and click on "submit garden for contest".
Easy way to get the Achievement:
Buy the "Almost Only a Garden" from the DLC (Thank you @XBJazzyGaming for confirming this plot). Then Go in the garden and buy following furniture:
1x Sofa Jamaica
2x Chair Jamaica
1x Table Jamaica
2x Couch Beto
1x Garden umbrella Nasofa
1x Carousel Asobi
1x Grill Fury
20x Ball Solar lamp
1x Alu Arbor
Hammock Melod or Drelod
Enter the Garden Contest and choose "American".
Check a smaller houses if house is not available, such as the "Camping Bungalo" as @Darklinkvortex recommended in the comments with the listed furniture and has shown to work.