The Enemies of Peaceful Rest Valley
The enemies in this area are extremely tough, so it pays to be well-prepared. Stock up on Hamburgers and Teddy Bears (to absorb damage) before heading on. It is a good idea to rest if you are low on HP and PP. Also, deposit all of your money in the ATM, so that if you die you don't lose any. When fighting here, take out the Spinning Robo first as it can do a great deal of damage to you. Save the Lil' UFO for last because it is tough to hit. The Mobile Sprouts will be easy for you. If you get a cold, heal by use PSI Healing α.
The most difficult enemy you'll fight is the Territorial Oak. While it is rather easy to defeat it has a last resort attack that can wipe you out instantly. When destroyed, the Oaks burst into flame causing usually mortal damage to Ness and destroying his Teddy Bear. To avoid this, run away from any Oaks you come across. Do not attempt to fight them at all. Use the disappearing enemies trick if you can't get past one. If you do decide to battle the Territorial Oak, you can reduce damage from its explosion by quickly pressing on your controller. While you will lose some life, you can still live and get slightly more experience than the other encounters.
Maneuvering Through the Valley
Once you re-enter Peaceful Rest Valley, head north past the broken bridge and back to the Pencil Statue. Use your newly acquired Pencil Eraser and voila, the statue is gone. You'll notice a bridge leading to the right and the path also continues north. Take the path north as far as you can for another photo opportunity before crossing the bridge.
Once across the bridge, head to the left and around the bend. Once around the hill you'll find a split. Head north to grab that present that you could see earlier for Travel Charm. Continue to the left and then south for another split. Take the split to the right but go straight south when you can. You'll come across a Luck Capsule in another present. Go back north and then take the left split and continue south again. Soon you'll pass by the broken bridge.
A little to the south of the bridge you'll find a present with a Croissant. Grab it and head southeast. Ignore the hill and continue to the east to find a present with a Bomb. Go back to the left, ignoring the hill that leads nowhere again, and head northeast. You'll come across another bridge, which you should cross. There is nothing to the south of the bridge, so just head straight north. You'll eventually come across another split. Make sure to take the left split first for a Hard Hat (a powerful defensive item). Equip the hat and head to the east. Take the right split now and head back south. You'll notice a house, which means you're on the right track.
If you take the left split while going south you'll come across a Cup of Noodles. Grab that and head back and take the right split. When you reach the cave, enter it and you'll soon be at Happy Happy Village.