You need to work through the main story until you at least have the IGNITION AXE.
What Will do I Need?
1) GRENADE LAUNCHER from the CHAMBER OF SECRETS.
2) At least one, and probably two, PRESSURE BOMB upgrades (for range).
3) The LONG-RANGE GRAPPLER from RONALD’S TREASURE CHAMBER.
How Do I Do It?
1 – Follow the story until you destroy the DEVICE OF DOOM in the Temple of the Destroyer.
2 – Light the three TREASURE BRAZIERS with the IGNITION AXE.
-The first is in the room above the Temple Entrance tube. Use the HOOK SHOT to latch onto the edge and pull yourself above the main entrance.
-The second is to the right of the Conveyor Maze tube. Awaken the golem with the IGNITION AXE.
-The third is above the left of the Golem Altar tube. Awaken the golem here too.
3 – Head back down to the Temple Bowels tube, drop down, and leave past the DEVICE OF DOOM room. Use the lever to access RONALD’S TREASURE CHAMBER and look for the false ceiling just above the trashium. Grab your three upgrade cogs and the LONG-RANGE GRAPPLER.
4 – Head to the Temple of Guidance. You can access this in the West Desert, through the door you escaped from way back at the start of the game, or by falling down the pits to the West.
5 – From the room where you picked up SPRINT HYDRAULICS, head right to several rooms and used the JACKHAMMER to break through the brick wall and access the Lower Temple Shaft tube.
6 – Head down and right, working around the stone structure to open the CHAMBER OF SECRETS. Complete this for the GRENADE LAUNCHER.
7 – While you’re here, complete the CHAMBER OF ARROWS and CHAMBER OF WHEELS to open access to the DEVICE OF DEVASTATION. Destroy it.
8 – Using your LONG-RANGE GRAPPLER, head right of the DEVICE OF DEVASTATION and use the shortcut to Yarrow.
9 – Work your way down to the area circled in red.
Use the GRENADE LAUNCHER to blow up the bouncing mushrooms, allowing you access to the rest of the area.
10 – Work your way down to AERONAUT’S STATION, making sure you unlock all the tubes along the way. Because you don’t have the JET ENGINE for this achievement, you will need to use PRESSURE BOMBS to work through the cave to the other side, allowing you to unlock access to the Mosquito Minefield and the DEVICE OF DISASTER. Blow it up.
11 – Final stretch. Make your way back to the Temple Bowels tube in the Temple of the Destroyer and get your platforming and grappling skills ready. With the LONG-RANGE GRAPPLER, you can latch onto the ceiling high above the lava section you’d normally use the JET ENGINE to fly over. Work your way right, past the drippers and golems, then drop down the loooooong shaft to The Grand Lava River tube. That’s the hard bit done.
12 – Work your way down through the rest of the Temple of the Destroyer, opening up the three tubes along the way. Once you get to the Inner Sanctum tube, it’s a few short grapels to the right to reach and destroy the DEVICE OF DESTRUCTION.
13 – Once done, the SEQUENCE BREAKER achievement should unlock immediately. Congrats!