Here is the full list of all 12 Logic Town achievements.
Help Otis throw a party
Help Drew locate every shipwreck
Help Peter unload the cargo ship
Help Daniel find "Esmeralda"
Help Agnes tidy every room in the hotel
Help Betty grow a garden
Help Simon invent a new cocktail
Help Phil rebuild the Royal Harbour Hotel
Help Becky open her new Bakery
Help Harold clear the train platform
Help Tobias create the perfect brew
Help Jack breathe new life into the picnic spot