So, obviously:
I won't provide a complete walkthrough, but if you read this guide closely, you'll wind up spoiling a lot of the backtracking that is (in my view) part of the fun of any metroidvania. I hope you let yourself play the game. I offer this guide mainly as a last resort for achievement-hunters and completionists. (The truly neurotic completionists, since Steam isn't even counting achievements for the game at the moment.)

If you're stuck and want a rough walkthrough: use the map below and always head toward the next Mech# and the next boss in alphabetical order, and you'll be on the right track. Push buttons, light lamps, and don't die.

There are 8 achievements:

• 5 = for defeating each boss, including the final boss (not on map). Health upgrades are key, but I don't offer specific strategies for each boss, except: upgraded Mech#2 deals a lot of damage.
  
• 1 = collect all Robodex files.
  
• 1 = 100% map completion.
  
• 1 = Buy all Mech upgrades. I have no special advice here: you need lots of coins.

On the left below is the inventory at 100% (minus one health upgrade... we'll get to that later).

On the right below is color-coding that indicates how I will represent each of these items on the map.

• Red "+" = Health upgrade (there is no achievement directly for collecting these)
• Blue # = Mech
• Yellow/Orange # = Robodex file
• Capital Letter = Boss

The map below shows the locations of nearly every item. The only thing missing is a single Health Upgrade, which you can find pretty easily near the end of the game. After you travel to the final area, go all the way to the right before breaking the glass and heading upwards into space. Again: collecting health upgrades doesn't directly unlock any achievement, it's just handy for boss fights.

(Robodex #s are based on positions in the "Trophy Room" that you'll eventually find. These #s do not prescribe an order for collecting them.)

If you prioritize getting the next Mech, you'll be able to get many Robodex files as soon as you see them. Some possible exceptions:

• You can't get Robodex #1 without Mech #6
  
• You can't get Robodex #2 without Mech #1, Mech #4, and Mech #7
  
• You can't get Robodex #3 without Mech #1
  
• You can't get Robodex #4 without Mech #6
  
• You can't get Robodex #9 without Mech #2
  
• You can't get Robodex #10 without either Mechs #1+#2, or Mech #4
  
• You can't get Robodex #11 without Mechs #1+#3
  
• You can't get Robodex #13 without Mech #7

You also cannot descend towards Robodex #5 and advance towards boss D unless you have Mech #7; that whole lower-left corner of the map is blocked off til the late game.

Yeah, this is the tricky bit. BIG THANKS to ErsatzDragon, Plutoneus (Dev), and PickleMaster for helping me understand this. This is the most explicit portion of this Guide, so I will throw it behind spoiler tags. If you don't want a spoiler: it is possible to get up there using exactly the mechs you would think you would need.

Get in position at the bottom of the long vertical shaft, and do the following. Below I refer to the controls on an Xbox controller.

• Use Mech #1's special ability to fully-prepare a speedyjump thinger (hold X on controller/keyboard)
  
• Jump: you will hold this down continuously throughout every step below (A on Xbox controller, Space on keyboard)
  
• While still mid-way through the speedyjump, access the menu and switch to Mech #4 (Right trigger on controller, "Z" on keyboard); continue holding down the jump button.
  
• While still holding down the jump button, use Mech #4's flame ability to propel yourself upward (tap X on controller/keyboard).
  
• Upon reaching the top, quickly switch to Mech #7, and hit the button to sound note C (Right bumper on controller, "A" key on keyboard)
  
• Fall to the bottom.
  
• Repeat first 4 steps above to get yourself back up to the Robodex.

The trick is that holding down the jump button retains more upward motion than you would otherwise have. This is pretty difficult to pin down in normal gameplay.