To complete the forest, you'll need to find all of Alice's dolls. The forest is separated into smaller segments, each segment ending with a magic circle guarding your way. You'll need to find all of the dolls in the previous segment in order to make the seal vanish.
Note that after you enter once, Rinnosuke's shop opens up next door. This means you can now access the vending machine (So you can now use the codes located on The Genius of Sappheiros: Miscellaneous), as well as item crafting. The Forest of Magic is also the first stage in which you can find items for crafting, and there's a lot of them you can find - not just chests, but enemies will begin dropping the items here too. Try to avoid dying so you don't have to go recollecting the many, many chests in the area, or lose out on drops!
Speaking of which, there are a couple moderately dangerous enemies here. The turtle-like enemies have a high defense and HP, and can protect their allies, making them the sole target of physical attacks for a turn, but they're not too dangerous on offense. The mushroom enemies counterattack with a column-targetting sleep effect, so try to use a formation that's spread out. The small computer-chip enemies are easy to kill, but have a move that can inflict paralysis on the whole party. And finally, the ice-lady enemies carry both a party-wide water spell that can do some significant damage, and the ability to charm your whole party, so be careful when fighting them.
Boss: Alice Margatroid
HP: 1500 (Regenerates 30 per turn)
Alice herself has relatively low capabilities, so she summons up doll formations to protect herself at the start of any turn in which she doesn't have any. She will randomly summon one of three doll formations at the start, and then whenever that formation is destroyed, she will summon the next formation (In the rotation of Defense -> Attack -> Elemental -> Defense). In general, her defenses have no weakness nor particular vulneurability, and she can be taken down if your whole party is focusing on her - however, if you neglect destroying a formation for too long, it will become much more dangerous. However, if you ignore Alice and focus on her formations, her HP regeneration will become an issue. Therefore, it's advised to have a team with a variety of capabilities, especially elemental variety (So Marisa, Patchouli, and even Nitori can be useful here) and to make an effort to stay on offense as much as possible. This is the game's first serious and difficult boss fight, so don't be surprised if it takes you a couple of attempts.
How To Negate Alice's HP Regeneration: Alice's HP regeneration can be safely ignored if you make use of Sakuya's abilities. She has an incredible ability called コロッセオワールド (Killing World). This will prevent ALL hp regeneration, including spells, for roughly 6 turns. The best way to use this is with conjunction with the 'Elemental Formation'. As the final doll is left, simply trigger Killing World and pound her into submission as her HP Regeneration and her potent healing spell is nullified! Of course this effect also affects your own healing spells. So make sure your team is fully buffed/healed before activating Killing World.
Defense Formation: Five dolls with 200 HP each are summoned, carrying shields. They all have excellent physical defenses and resistances, and also resist Light and Dark spells. They will make weak attacks that can cause status effects to your party, while Alice supports them with more ailment spells of her own. If left alone for too long, these attacks will stop being just slight irritation and become dangerous; thankfully, this formation might be easiest to take down. They're very vulneurable to any form of elemental magic, especially earth. Patchouli's earth spell can probably 1HKO the entire formation, or leave them at least very close to death.
Attack Formation: Three dolls in a triangle formation, again with 200 HP each. These dolls have no actual defensive stats, but carry massive resistance to dark, light, and physical damage elements. They make simple physical attacks which, all the same, pack something of a punch. After a couple of turns, they will gain random-targetting multi-shot attacks, and if left much longer, Alice will buff her and her dolls' attack power, at which point they will tear your party apart. However, they all carry an enormous weakness to the four elements, and no Magic resistance, so Patchouli, Marisa, and even Sanae's spells will be very powerful here. Something that works really well here is to use Sanae's スカイサーペント (Sky Serpent) on Alice to get rid of two dolls, then use Marisa's electricity spell to kill the last doll.
Elemental Formation: Four dolls, each color coded to one element (Fire, Water, Earth, and Lightning), this time with 300 HP each and 33 HP recovery with matching land. These dolls cast single-target attack spells of their corresponding element, and if a spell of the matching element hits them, they will counterattack with a spell on your whole party. They're all resistant to Light, Dark, and all physical elements, and nearly immune to damage from their own elements, but weak to their opposing elements. Since they don't carry any resistance to the other two elements, once you kill one, group-targetting elemental spells become an option. Beware of leaving this formation for too long; after a while, Alice will begin to cast a healing spell at the end of each turn which will heal her and one of her dolls for ~70 HP, in addition to her normal regeneration. If left longer, she will buff the party's magic attack power, making their spells very dangerous, especially as they may have affected the land values. Players who can deal with this, however, may find that leaving a single doll alive during this phase and focusing fully on Alice might be easier than going between formations.
After this battle, Alice will join your party.