This is basically just one huge dungeon chapter. So unless you have some unfinished business to take care of the Skyhold is the only place you have to be in. There is one particular location that you can visit however, it's called the Chompsire. It's located right in the middle of the forest to just a wee bit southeast of the Skyhold, on the small piece of land jutting out at the very edge of the landmass. In this village is an equipment shop that sells element-resistant accessories, and a magic shop that sells level 6 spells.
Also, if you were to return here in Chapter 5, the equipment shop will also be selling all the second-best weapons in the game for 200,000 each. The item shop carries elixirs for 50,000 apiece. Look around and see what you need then return to the Skyhold.
Skyhold Outer Keep
Outer Keep 1F: Pull the switch on the left to take the left down, then circle around to the southeast for an Arctic Wind and an X-Potion at the end of the north corridor. Operate the lift in the middle to go back up. Go toward the southeast edge next for a Phoenix Down, then use the lift to the east to go down. Run up the stairs up north to grab the Divine Fists. Take the southeast lift up to a Light Curtain and move on upstairs to 2F.
Outer Keep 2F: You begin this floor on the upper catwalks. Head down along the middle path to a chest with 5000 pg inside. Next, use the right lift in the middle of the area first to go down. Run to the southeast corner for a Turbo Ether, then head for the bottom middle path to find a Gold Hourglass. Follow one of the paths going left and you'll get a Bomb Arm at the southwest corner. Go back to the center and climb the stairs for a Spider Web. Descend to the other side to score a Tengu Sneeze, Go back down to the middle of the area and use the lift on the left. Go to the northwest corner and back to 1F.
Outer Keep 1F: Grab the Venture Badge here, Save then head for the exit. Enter the Prison and approach the goal marker for a scene, to be followed soon after by a boss battle.
Boss Battle - Revenant
Once again here is another boss who has grunts for company, and is especially annoying due to his ability to possess your characters and take control of them. The grunts are susceptible to lightning so focus on taking out two (particularly the one with the shield and the one with the staff), and leave just one so the boss will not call for reinforcements. For the Revenant himself, you can have your Time Mage cast Stop to freeze him (adding Stop as status attack to your weapon also works). He is also weak to light, so cast Shininghead and Harpoon with the Shamanism command for your main fighters then just have them attack. Cast Hastega on your party too if you can use it.
You will be rewarded with the Guardian Asterisk for defeating Revenant. Go back to where the adventurer was and go through the north exit, to proceed to the main area.
Skyhold Inner Keep
Inner Keep 1F: Begin by activating the top lift in the middle of the area then go left for a Bacchus Wine. Head back down to the middle and use lift to the left this time, then go straight up down the stairs for an Earth Mallet. Return to the lower area one more time and use the right lift. Head up and left down the stairs to the northwest corner to 2F.
Inner Keep 2F: Go east on the first corridor that you upon entering the area to pick up 4000 pg. Turn around to follow the middle corridor up the stairs and go south for a Teleport Stone. Use the lift at the other side to go down. From here, go along the corridors until you get to the upper catwalk on the west side to grab a Remedy. Next, search for a way to the bottom-middle section of the lower floor, where you'll find two lifts.Take the right lift up and descend on the first stairs to the right for some Hermes Sandals. Head straight up from here and descend the stairs so you can continue back down to 1F. Pick up a Gladius from a treasure chest there and return yo 2F. Now, look for a path along the lower level that will lead to the steps at southwest corner onto 3F.
Inner Keep 3F: Head east toward the objective marker for a scene and a boss battle.
Boss Battle - Janne
Janne's move set is limited to that of a Fencer as usual, but you'll want buff your party's physical defense as his attacks can get pretty brutal. Add piercing capability to your attacks with Harpoon and if you have a Time Mage, cast Haste on your main fighters. Janne's magic defense is not very good, so it's worth taking advantage of by casting buffed high-level elemental magic. Also, the best time to attack is when your opponent is in Wolf Stance. Because hitting him while in Aurochs Stance will cause him to counter with Stamped, which can be painful..Healers should use Vivify or Benediction to heal.
Moving, use the lift and continue down the stairs to the left. Go up the corridor to the far left for a Lilith's Kiss, while on the opposite end of the same corridor is a Remedy. Take the stairs at the southeast corner back to 2F, grab the Lustrous Shield and return to 3F. There, proceed to the northwest corner on the lower path to get a Luminous Robe. Climb up the nearby stairs next for 6000 pg. Use the lift to the right so you can reach the center of the area. Now make sure you are truly ready before going through that doorway, because you are now at a point of no return. Rest and save before moving on.
Boss Battle - Anne
The fairy is weak to fire so add the element to your attack with Firehead and also cast Harpoon. Black Mages should keep using Fira or Firaga. While the Time Mage uses Hastega on the party. Anne has a move that can do a lot of damage and Poison your party at the same time. Either remove the ailment with items or spells or simply compensate by using high-level healing spells such as Benediction on your entire party at once. At some point during the battle, Anne will create six copies of herself, and they will counterattack every time you hit a fake. The best way to get around this is to wait for Anne to buff herself with status enhancements. That way you can tell which one is real from the target list on the touch screen. You can steal Elixirs from her as well.
Once Anne is defeated, warp out of the dungeon and land on any piece of dry land on the world map. Watch the scene, after which the game informs you that New Game + is now available. Now make sure your party is in top condition and properly geared up, before you save and return to the title screen. That should be all there is to this chapter.