The LEGO Movie Videogame

In case blew up all the fire locations in free roam, like me, this solution is for you!

Start up level 10 "Infiltrate The Octan Tower" (the last one in Cloud Cuckoo Land) and you should start on the pirate ship. Look for the small gray piece with a fire icon on it near where you start and where the water is coming overboard. Select Kabob Bob for your character, stand by the fire icon and press B.

This achievement can be gotten fairly early in the game. You will need a fire-starting spot and a character capable of making a fire. Just have your fire starter stand on the fire icon on the ground and then press the button when you are prompted to do so.

The first opportunity you will have to do this is in "The Old West" hub area after you have acquired Wiley Fusebot. (You will get Wiley after completing the first "Old West" story.)

The fire starting point is part of the "Catch the Bank Robbers" task, so you will need to have that task first. If you don't, just go to the front of the bank and talk to the banker in front of the open safe. The fire starting point is close to there -- about five steps from the bank door in front of the chicken fence! But you may need to prepare it first: jump on the boxes on the opposite side of the barn, enter the barn's loft and then push the box of debris off the second story. Jump down, clear the mess and you will see the fire starter symbol on the ground. It looks like red and orange flames on a gray, square plate.

Now change to Wiley Fusebot, step on the plate and press . Congratulations! You've just popped the Achievement.

EDITS:

I've added a link I found on YouTube that shows my solution. Thanks to packattack04082 for providing the video.

If you've already used up your hub fire starter spots by exploding them, there are a couple of spots in the free play chapters that re-spawn on each play-through. See Vestride's answer for one of the locations.

This can be attained at the beginning of the tenth level: "Infiltrate the Octan Tower".

When the level loads up go to the top right of the deck and in front of the door is a square with a fire logo on it.

Select a character that can make fire and press (B).

List of fire making characters:
Caveman (Unlocks after Level 8, costs 100,000)
Kabob Bob (Unlocks after Level 14, costs 10,000)
Lady Libery (Unlock code: A76DN7)
Native (Unlocks after Level 3, costs 100,000)
Tomahawk (Unlocks after Level 4, costs 150,000)
Wiley Fusebot (Unlocks after Level 3, costs 125,000)

*Note: This was done in Free Play mode, it can't be done in Story mode.