At the side of the castle there's a chest, grab it.
Go into the castle through the courtyard, straight ahead, past the first two sets of stairs and up either of the second set of stairs to the Queen's room.
After talking to the Queen, exit the throne room and go out the door on the Eastern wing.
There's a little nook to the East - go through it to find the Scroll Dealer who gives you a free Heal Omega Scroll.
Go to the previous screen then North. In this room you'll find a Potion Omega in the Pot.
Downstairs there's a secret passage in the South wall that leads to a couple nice swords.
Exiting this area, locate the Second Chance behind the castle.
Now in the North Western corner of the castle is the shop. You'll want to buy the armour, but the Jade Sword you found in the secret passage is better (has higher Luck) than the Onyx Blade.
You'll want to be maxed out before tackling the mountains (999 HP.) Go back to the first area of the desert (but don't scroll offscreen or you'll have to play through the desert again) and do a few battles.
I recommend you have at least 30 Elixir, 15 Holy Water and 20 Potion Omega before heading into the mountains. More never hurts if it's your first time!
Now go back to the room with the beds, sleep, and save.