Aegis drops from the same chest as the Holy Ring. Just immediately go left and north when you reach the 2nd section.
Ribbon and Futsu-no-Mitama drop from the chest Cure Ring would normally be in. The chest deep south of the 2nd section.

Raise ring is in the 1st map, the chest at the top of the middle part (red sahagins guard it). The holy ring is in the 2nd area go left right at the start of the area, you only have to go past 2 of the less deadlier sahagins to get to it

Hey Soulgun, from which chest exactly did you get Raise ring in foggy swamp? 1rst area? 2nd or 3rd area?

I found a Holy Ring and Aegis (+5 def) on my first run through.

Can confirm raise ring drops here also, random chance from chest.

Chest 16: Dark Matter, Ribon, Rune Bell and Futsu-no-Mitama (+7 Str Artifact), Chest X (near mob 15 in original map): Rat's Rail. Giant's Glove, Wonder Bangle and Mjollnir, I stop at 4 Rewards per chest so IDK if there are more

 Click to Enlarge

Ok Igot all 4 Rewards from all chests, Chest 4: Dark Matter, Ring of Blizzard, Noah's Lute and Donny's Crystal (Lilty Memory Crystal), Chest 2: Sasuke Bñade, Sage Staff, Loaded Dice, Noah's Lute (can get a Mythril or Electrum with Artifact)

 Click to Enlarge

I'm doing this dungeon, using the Original Map, in Chest 2 I got Sasuke Blade(and a Mithyrl), Chest 4 Dark Matter, Chest 16 Ribbon and Chest Near Enemy 15 (chest X) Rat's Tail.