This guide will teach you how to get past all of the Sun Doors in the Ancient Mana Workshop map of Atelier Ryza 2: Lost Legends & the Secret Fairy. These doors block your progression with the main story.
You should have the Lantern at this point. Use the Lantern to light all of the Lantern Pillars in the Corroded Mine Cavern map, and possibly even the area before that (it might have one Lantern Pillar, but unsure). Lighting them all up will unlock the Sun Door for this area.
You’ll meet another Sun Door in the Fairystone Eaters’ Domain map. Unfortunately, it’s not as simple as lighting up Pillar Lanterns to advance further. You’ll have to collect the memories throughout the Ancient Mana Workshop and complete them to get the ‘Crafting a Custom Flame Crystal’ recipe reward.
Go back to your house and craft the item. You should have sufficient materials to craft the Custom Flame Crystal around this point of the game; if for some reason you don’t, they can all be found at the Ancient Mana Workshop area. After crafting the item, go back to the Corroded Mine Cavern and trigger the cutscene. The Sun Door should now open, so go back to the Fairystone Eaters’ Domain and proceed with the main story campaign.
Extra useful notes:
Previous areas you couldn’t access before to get memories should now be accessible in the Fire People’s Village and Fairystone Eaters’ Domain. A tree blocking a vine on the wall should be gone in Fire People’s Village. Climb it, collect the memory, get to the next area by pressing A by the edge of the broken floor, and collect the (last) memory fragment.
Fast travel to the Fairystone Eaters’ Domain and the areas should now be accessible like the Fire Peoples’ Village. There are 5 memory fragments to collect here. The first three will be on the right-hand side of the map upon entering the area. Keep moving in the same direction and you’ll eventually come across these memory fragments. The last one you can get right now is found at the bottom-right corner of the map; a tree was once blocking the area and you can press A to get to the other side from the edge. After getting it, you’ll need to continue the story and fight the boss before you get can the last, most important fragment.