There are a total of 16 purple chests in vanilla Shadows of Adam, and 20 if you have the DLC. These chests are hidden in Dungeons and towns. Only 2 of the chests are permanently missable, and they have been identified as such. The first section will contain a simple list of the chest and area found, for those who want minimal spoliers. The second section will contain details of what is in each chest, general directions on how to find them, and screenshots of the locations.

Please note that this list is in the most likely order. Some areas need to be visited again later.

1. The Tangle [Missable]
   
2. Misty Woods
   
3. Wind Tower
   
4. Wind Tower
   
5. Haunted Swamp
   
6. Water Garden
   
7. Passage [Missable]
   
8. Firmus
   
9. Magma Cavern
   
10. Ruins of Lod
    
11. Earth Maze
    
12. Dradora
    
13. Dradora
    
14. Contested Island
    
15. The Lost Cave
    
16. DLC ONLY - Mystic Cave
    
17. DLC ONLY - Mystic Cave
    
18. DLC ONLY - Mystic Cave
    
19. DLC ONLY - Mystic Cave
    
20. Wraith Abyss

Please note this list is in the most likely order. Once you get the airship numbers 12-20 can be done in other orders, but this represents the easiest progression.

1. The Tangle - Thorn Sword
   You will see it out in the open. Climb up the partially obscured vine. Note this chest is missable.
   
   
2. Misty Woods - Magician Rod
   In the section where you chase the wraithling, notice a passage in the trees in the top right.
   
3. Wind Tower - Star Rod
   Drop down from the left side of the 6th floor.
   
4. Wind Tower (Grotto) - Chakra Claw
   Drop into the grotto from the right side of the 5th floor.
   
5. Haunted Swamp - Phantom Darts
   After the graveyard, hop to the right path and head up.
   
6. Water Garden - Thunder Rod
   Head down after coming out of the first grotto section.
   
7. Passage - Ice Sword
   Solve the orb puzzle and ride the cart to the platform. Note this chest is missable.
   
8. Firmus - Ice Claw
   In the cave with two entrances, there is a hidden passage beneath the pool on the right.
   
9. Magma Cavern - Tiki Darts
   In the section with holes, drop from the left side.
   
10. Ruins of Lod - Sky Claw
    Head up the stairs to the top of the tower.
    
11. Earth Maze - Fire Rod
    There is a secret path in the bottom right of the large crystal room.
    
12. Dradora - Torchflame
    Defeat Pendragos and win the dice game against Headhunter.
    
13. Dradora - Spearheads
    Defeat Pendragos and win the dice game against Headhunter.
    
14. Contested Island - Raider Ripper
    Secret passage behind highest house. Requires completion of Contested Island quest.
    
15. The Lost Cave - Legend Sword
    Take the right path from the entrance.
    
16. Mystic Cave - Vapor Clasp
    DLC ONLY - Defeat the boss of the Mystic Cave.
    
17. Mystic Cave - Mindreaver
    DLC ONLY - Defeat the boss of the Mystic Cave.
    
18. Mystic Cave - Aether Ring
    DLC ONLY - Defeat the boss of the Mystic Cave.
    
19. Mystic Cave - Lodestone
    DLC ONLY - Defeat the boss of the Mystic Cave.
    
20. Wraith Abyss - Crystal Sword
    In the tower section. Drop to the teleporter from the left side.
    

Thanks for checking out this guide. I wanted to create it because there didn't seem to be any comprehensive guide of purple chest locations with pictures for reference. I may expand the guide later to include other useful items, juice locations, essence locations, and possibly more.