To get this achievement you must do the following:
-Collect all 32 Heart Squids (Your choice if you convert them into Hearts)
-Collect all 20 Dark Magic
-Purchase all Skills & Upgrades from the Shop (which will cost you 2300 Gems in total, and you can carry a maximum of 999 at a time)
++Shampoo x3 (50, 150, 300)
++Silky Cream x3 (50, 150, 300)
++Pistol Tune Up x3 (100, 150, 200) (Available from the start of Pirate Mode)
++Scimitar Polish (200) (Available from the start of Pirate Mode)
++Backdash (100)
++Recover (150)
++Power Kick (400)
-Beat the game in under 3 hours. (You get one more hour than for the Any% Speed Run)
As a rule of thumb, do this one in Pirate Mode (unlocked after clearing the game once) as you'll start with all the Pirate Items, allowing you to save a lot of time by being able to collect anything as soon as you reach it (barring parts blocked by story events).
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As an alternative method to following this walkthrough, if you have an Any% Speedrun save that has at least 15 minutes to spare then you could just run through and collect the rest of the items & upgrades/abilities on that one. (That's how I got this one, with less that 2 minutes left when I got the achievement!)
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Walkthrough, minimum path instructions
Scuttle Town
-Dark Magic x1 (Story battle)
-Library Card (from Sky)
-Heart Squid x1 (In Squidsmith's building)
West Path (To Lighthouse and beyond)
-Dark Magic x2 (One requires Boots, Hat, and Cannon)
-Heart Squid x1
East Path (to Scuttle Palace)
-Heart Squid x3 (2 are higher up)
-Dark Magic x1 (Hidden room, higher up)
Scuttle Palace Front + Sewer:
-Get 3 Flesh Pops (Drops from Snakes in Sewers)
-Dark Magic x1 (Boots needed)
-Heart Squid x1
-Get Travel Brochure
-Turn in Flesh Pops to Bolo for Gate Key
-Turn in Travel Brochure to Squid Baron for the Squid Oil
Scuttle Palace:
-Get Forbidden Isles Map
Saliva Island
-Heart Squid x1 (Pistol)
-Get Metal Ring
-Get Ham Stink
-Use Metal Ring to get up to Lummox
-Dark Magic x2 (First is found by going past the Lummox, second is on the way down to get the Petrify Spell, in a secret room; hold left while falling to enter the wall)
-Drop down to get Petrify Spell
-Give Petrify Spell to Man
Saliva Island Cave
-Get Key to open door to reach Cyclops Plant
-Heart Squid x3
-Defeat Cyclops Plant for Spiderweb Island Map
Spiderweb Island
-Dark Magic x1 (Scimitar)
-Get Fossil
-Heart Squid x1 (Scimitar)
-Carry Rottytops through maze; this can be a potential time sink, so make sure to only do it in a single run! (See my guide for that to speed through it:
https://steamcommunity.com/sharedfiles/filedetails/?id=......)
-Heart Squid x1
-Give Squid Oil to Poe to get the Shriveled Thing
-Dark Magic x2 (First is long jump across from the Spider's Cave, the other is right by the Spider's Cave)
-Use Shriveled Thing to gain entry to Spiderweb Island Cave
Spiderweb Island Cave
-Key x2 (One to access a Power Unit, one to gain entry to Empress Spider)
-Activate the three Power Units
-Heart Squid x3 (One requires a hidden Plant Launcher, found down beneath it)
-Defeat Empress Spider for Tan Line Island Map
Tan Line Island
-Get X-Ray Specs
-Get Mummy Sketch
-Get Enchanted Blade
(Return to Saliva Island)
-Heart Squid x1 (Along the way to the Mummy Sketch)
-Get Mummy Sketch
(Return to Scuttle Island)
-Get Mummy Sketch (Now you have the Password to the Tan Line Palace)
-Trade Fossil for Death Mask
-Give Enchanted Blade to Brandon (Optional, this can be done later when you return to talk to Ammo Baron)
(Return to Tan Line Island)
-Enter Password to Tan Line Palace
-Sneak through the Palace, collect 3 Keys and free Rottytops, Sky, and Risky Boots to get the Golden Pickaxe.
[After getting your Gear back is a GREAT time to hit the best Gem farm in the game to get to x999 Gems for when you next get to Scuttle Town for shopping]
-Heart Squid x1
-Dark Magic x1 (Can't be collected until after you have your Gear)
-Give the Golden Pickaxe to workers to clear the way on the island and access Tan Line Island Cave
-Dark Magic x3 (First is a Boots rush, one in a lower area, one accessed by Scimitar)
Tan Line Island Cave
-Heart Squid x3 (One is hidden in the path you break through with the Scimitar to reach Squid Baron, it's in the very bottom-left corner)
-Defeat Squid Baron for Mud Bog Island Map
Mud Bog Island
-Heart Squid x1
-Dark Magic x1
-Use Death Mask to enter City of Lost Souls
-Heart Squid x1 (Boots rush)
-Dark Magic x1
-Get Green Coin, Red Coin, and Blue Coin
-Heart Squid x1 (Boots Rush; use the switch to add a platform to get enough distance)
-Dark Magic x1
-Give coins and beat the Color Trio to get the Golden Locket
-Give Golden Locket to "Rottytops" for the Hopeful Flame
-Use the Hopeful Flame to get the Manly Musk
-Use Manly Musk to enter Mud Bog Island Cave
Mud Bog Island Cave
-Heart Squid x3 (Two are along a very long path, will require Key x1)
-Defeat Dagron to get the Frostbite Island Map
(Return to City of Lost Souls)
-Get Lost Soul from "Rottytops"
(Return to Spiderweb Island
-Talk to Rottytops to identify Lost Soul as Spirit of Joe
Frostbite Island
-Dark Magic x1 (Boots rush, ram a wall)
-Meet Ammo Baron and Techno Baron
-Dark Magic x1
-Heart Squid x2 (First is in a giant room with three Launcher Plants near the entrance, the pattern is: Middle, Down, Left; the second one is along the way to Bolo and requires Cannon)
-Dark Magic x1
-Get the Targeting Module from Bolo
-Heart Squid x1 (Cannon)
(Return to Scuttle Island)
-Talk to Ammo Baron
-Give Spirit of Joe back to Joe
-Give Enchanted Blade to Brandon (If you didn't already do it in your earlier visit)
-Talk to Ammo Baron to fire the cannon and open the Frostbite Island Cave
(Return to Frostbite Island)
Frostbite Island Cave
-Key x1 (by where you enter)
-Heart Squid x1 (Near a Key)
-Key x1 (near a Heart Squid)
-Heart Squid x1 (Use a Key to follow a roundabout path to reach it)
-Key x1 (Path to the right of the Heart Squid)
-Enter path to the Steel Maggot, picking up the final needed Key along the way.
-Heart Squid x1
-Defeat Steel Maggot for the Lonely Grave Map
Lonely Grave
-Witness the unleashing of the Pirate Master kidnapping Risky Boots
(Return to Scuttle Island)
-Trade in your Heart Squids for extra Hearts (If you want, it's optional)
-Do any remaining shopping for the required upgrades and maxing out any needed items for the final battle (especially Bubble Shields).
-Head to the now-renamed Pirate Master's Palace and enjoy his difficulty-spike maze of death (OR use the Out Of Bounds glitch to just fly up to the final door leading to the big fight).
-Beat up the Pirate Master, trash his True Form and enjoy the Good Ending and your Achievement!