Northern Shards

• In the dungeon to the far left, marked by a titan hand at the entrance, you'll find one hidden in a room to the left of a small area in which you fight a few birdmen.
  
• After shard 1, just keep going, the other is at the end of the dungeon path.
  
• One in dungeon to the left that you teleport to - just follow it to the end.
  
• One on the top of the mountain to the immediate right of the large machine
  
• In the 3 shard door, when you arrive at the room with the two bird wizards and several birdmen and slime (just following the area where you dash north over the long pit) there is a hidden exit on the south left side of the room.
  
• In the small village on the stairs up to the primary northern village is an exit in the SE corner which only opens up after beating the boss- go through the little labrynth within to get another.
  
• On a ledge on the stairs south of the warp pad that has a large red flag on the northern most part of it. To the east of the flag you can see a beacon which can be activated via laser sighted rifle.
  
• At the village with the dogs, just before you enter the cave after climbing the stairs, there is a secret area left of the archway into the dog area. From there an obvious platform to the left exists- look south from that platform to find invisible platforms and your shard

Eastern Shards

• On the path to the Eastern area you'll enter a dungeon with an elevator- as you come down there are stairs leading down. There's an obvious set of platforms below them that leads west to the shard
  
• East from the warp pad, in the dungeon you find at the end of the path you'll have a big fight with several large plant monsters. After killing them take the upper path and follow it around to another shard
  
• After shard two, as you continue through the dungeon you'll go down another level and wind up at another large fight, to the left after the fight is a 1-key door on the southern left wall- follow that through to the end for another shard.
  
• In the door to the immediate south west of the warp pad, follow the dungeon through its natural course and you'll get a shard.
  
• To the left of the titan is a long platform, on the very northern section turn west and blast the pillar at the edge of the screen to activate secret platforms to a simple dungeon where another shard waits
  
• As you follow the path back from the titan via the south route you'll fight a large battle- from there take the southern path. You'll run into a door to open nearby the warp pad (E then immediately N from the warp pad). After dashing across all the fire pads at the end of the path there's a hidden button behind the pillar in the center of the area you land on which activates a hidden platform giving you access to the shard NE of it.
  
• After you press the floor button opening up the path to the area boss, turn around and head down the stairs immediately to your west. At the bottom of the stairwell you come down you'll notice a hidden 3-key door to the immediate north which will eventually lead you to the shard in the southwest corner of the area it leads to.
  
• After defeating the boss, as you're headed out from the machine room you'll find this one on the path

West Shards

• After leaving town, and crossing the bridge, head to the south west- you'll find a small bush just in front of a secret area to the W.
  
• On the path to the western area, after going through the first door and out, you'll be in a large area with a western and southern path. To the far SE side there is a small rock ledge that can be seen, identifying a secret exit to the E.
  
• In the dungeon to the north of the warp pad you'll come across an area blocked off by several machines next to a large crystal golem, if you head to the room west you'll see a post that can be slashed to lower them. Head back and follow the path to where there are six cells. In the third cell on the top there's a hidden exit in the top right.
  
• After going up the stairs west of the warp pad immediately go south through the forest where the crystal dog statue is- from there, invisible platforms.
  
• After entering the western path dungeon, just past the long line of cells along the lower section you'll come to a bend to the east then immediately to the north, on the bottom right of the bend back north there's a hidden exit to the east.
  
• After exiting the western path dungeon, in the NW corner of the map is a set of crystals you can destroy and go north through the trees.
  
• After going through the 3-shard door, there's a path in the northmost part of the area that leads east and around. Once you're in the dead guy's place, smash up his boxes to find this shard (you can easily spot the elevator you're trying to get to from the eastern side of the map as you move north)
  
• After following the main path you'll eventually come to a large open area with a central western exit (an area that looks like a ruined city)- take the SW exit instead, and follow the path around until it seems like a dead end in the SW- in the center of the building on the right at the end of the path is a hidden exit E then N to get the last shard.

Southern Shards

• After activating the warp pad, take the central western dungeon pad down- follow the dungeon to its conclusion to get your shard.
  
• Return to that dungeon and take the 1-shard door, follow the path like normal to come across your next shard
  
• As you continue past shard 2 you'll find an area with two force doors- one left and one top. Activate the switch through the left door then go through the top door to the far north where there's a floor button. After hitting the floor button follow the path all the way SE around a ledge to an area that you can follow and eventually wind up at another shard.
  
• After shard 3, keep following the path like normal, you'll fight a boss after which there's a shard
  
• Take the NE dungeon and follow the bottom left path through to the end, after a boss fight you'll get your shard
  
• Take the NE dungeon again, this time going right- through the 1-shard door you'll come to a series of platforms, the next shard is in the upper west corner for this area via some invisible platforms immediately to the west of a gun pillar
  
• As you follow the NE dungeon you'll eventually reach an elevator that takes you down to a room with two areas blocked by force doors, the one on the right that leads up and around features a shard
  
• After defeating the area boss, and returning to the south warp stone, head to the far SW corner of the map- you'll see a small block of ledge you can dash to, from there there's a set of invisible platforms leading down to a dash puzzle which features a shard

The primary reason for gathering the shards is to unlock doors that require all eight of them. Doing so will, normally, lead to a very large battle. The culmination of which will either give you an additional weapon or another outfit to use. You can find one such door in each of the four areas.

[EDIT]

I presumed originally that an additional scene of the game required all the shards in order to see. According to comments, it can be accessed just completing the game normally. Unfortunately, I did not experience the same effect. It wasn't until I had collected all of the shards on a NG+ run that I saw it. So your results might vary. You can find that scene after completing the game by going to the 'load game' option and you'll see an icon to the right of your save file that you can select.

What is it?

For those that want to know without doing the work:

The scene takes place presumably well after you slay the final boss. In it, your decayed skeleton is seen sitting against that odd monument (the one you lean against when you beat the game) within a cave. Next to you lies your little fairy robot, long since deactivated/decayed itself. It's a somber scene, and suggests you have been long since forgotten. It also suggests that perhaps the very last scene, where you're standing on the lake, as the Anubis-like dog leaves, never actually happened. That instead, that was your last vision as you faded into the embrace of death.