From the main menu, select "Speedrun". We're using the speed run mode because the Cola Syrup item is already unlocked there. Once you've loaded into the game, equip the Cola Syrup tactical item. Close the menu and throw it at yourself.

Start the "Laboratory: Base Level" level and continue through many areas until you arrive at the one which teaches you how to use the grapple. This is the last area in this level.

Go to the end of the level and speak with the NPC, then traverse back to the beginning to find the chest.

Start the "J-lab Factory" level and continue through the stages until you get to the merchant.

At the start of the next stage, head towards the left of the screen to reveal the hidden door to the "Saw Challenge". Complete it and open the chest to unlock the achievement.

Choose the "City Center" level from the mission select, then continue through a number of stages until you get to the one which has a downward-sloping zip-line with two aerial enemies shooting at you. You will notice that above is a vertical grapple point. Jump off the downward-sloping zip-line and grapple the bar above it, allowing you to discover the secret entrance.

The secret level itself is very straightforward. Once you obtain the item and exit the area, the achievement will pop.



Choose the "City Center" level from the mission select and continue until you arrive at in the sewer. There is a grate you need to shoot or explode open, then run through the sewer water to enter the secret area.

Complete the secret area, open the chest, and exit the area to unlock the achievement.

Start the Mysterious Desert mission and equip the umbrella. Continue through the level until you get to the stage where you go up a few walls, then have some room on the left side of the screen. Jump leftwards and activate the umbrella, gliding into the secret entrance.

Complete the secret stages, open the chest, and exit the secret level to unlock the achievement.

Or "Lengendary Plumber"

Choose the "Inside the Ruins" level from the mission select. Get to the stage in the video and use the umbrella item to clear the gap. I also had double jump equipped. Once you clear the secret mission and leave the stage, the achievement will pop.



Start "Inside the Ruins" level and continue until you're forced to use the bird vehicle. Shortly after getting past the first obstacles, you will be able to shoot a wall which opens a hidden door in the ceiling. Go through the open ceiling to enter the secret stages.

Tap the jump button to go up and don't hit the obstacles!

Also "Qungfu Master"

This secret area is located in the first stage of the Airship Core mission.

Near the end of the stage, you will be able to see a couple lasers guarding an area. I was able to get through them by bumping into them, receiving damage, becoming invulnerable from the damage, and running through the lasers.

Complete the stage, open the chest, and leave to unlock the achievement.

Tips for completing the level:

• You can shoot the spiky laser balls to trigger them to open up.
  
• Jumping and shooting the ground will propel you upwards a short distance.