Hi, I decided to post a thread about this since I haven't found any discussions on this goal, and I myself, had trouble with this goal.
Okay so the Baron offers you his pig 'Sir Pigglesworth' if you find all 3 rare items, the Golden Egg, the Golden Nugget, and the Golden Apple.
The first two aren't very hard to find if you're pretty patient.
The Golden Egg- get a chicken at the market ( tap market in the lower right corner of the screen and go to nature> animals> chicken) Chickens are quite in this game compared to other items. (Believe me) They are 750 royal coins (you're not spending your real money).Feed them until they grow into an adult chicken and after some time they WILL lay a golden egg.
The Golden Nugget- Get a mine at the market they will be under buildings>resources. You can either pick a sparkling mine or (maybe deep mine?I'm not sure.) If you're still early in the game your only option is the sparkling mine ($4,800 royal coins. No, it's not cheap but it's pretty easy to earn royal coins in this game from collecting money from buildings, fishing, taking care of animals, etc. ) which was where I got mine. After a few collections a golden nugget will be collected.
The Golden Apple- This is the hard one. I know some of you might argue with me, but to me this is hard. The Baron says could this fall from a tree? And I started chopping every tree I found but didn't get it. The ONLY tree which will have the golden apple is the apple tree.The apple tree costs 90 gems- and gems are not easy to get.
Places you can get gems:
-Sometimes, the market will have 'requests' and you have to give them whatever item with a big number to them for only a limited time, which is VERY hard but you will get gems.
-Another way is to complete some tasks for the Baron and sometimes he'll give you gems.
-Or buy a castle which is also very expensive( You can either get a king's keep or queens court they produce the same amount of royal points is the same it doesn't matter which one you get.) You can complete quests and sometimes will earn gems and other miscellaneous items.
-But if you can't wait, you can spend your real money to buy gems but I never do that because I'd rather spend my money on other necessities in real life.
Eventually, you WILL get the apple tree don't worry! In fact, you'll need it to cure Thurston ( the prince with allergies sneezing in a corner in boxers if you haven't already unlocked that expansion.) But I suggest to do other goals FIRST instead of focusing all your time into this goal.
If you have any questions feel free to comment or comment on my wall in castle story my ID is g00dvibes_ and my kingdom name is Elysia. I'm on there practically everyday and writing on my wall there would probably answer your questions faster.
I hope this was helpful! :~)