Are you talking about Rune Praga or Sharance Maze? If the former, you need the four golden vegetables and their regular versions as well, all giants, but they can be skipped and come back to later as they are not required to advance the story. If the latter, there are no requirements.
You can go through the entire dungeon without opening the doors and you can advance like normal. The vegetable doors are just treasure rooms, but they're great treasure rooms so I wouldn't advise skipping them. I've gotten them, but it's been so long I don't remember what's in the chests.
