Great Balls o' Fire looks like an Achievement that simply needs a good luck with the Random Number Generator. This isn't entirely so.

Achievement description says:

Both Multiball and Fireball modifiers are received by catching boxes that fall seemingly randomly from the destroyed robots. To get the achievement, you have to grab Multiball first and keep the balls alive until you get the Fireball modifier.

Thus the achievement description is actually slightly inaccurate. Namely, if you pick Fireball modifier first and the Multiball second, only one ball will have the Fireball modifier. One is not Multiball, so that's why you have to get them in a specific order.

Bear in mind that you need to have all three balls when grabbing the Fireball modifier or it won't qualify for the achievement (thanks to ERROR for pointing this out!).

So, let's look into tips and my trump cards: in what levels can you try this.

Boxes that grant you modifiers are called Power Cells. Their Codex entry states the following:

Power Cell: On certain levels exploding droids will drop these cells which provide a temporary power boost to the ionball, either creating multiple clones or a super-powerful ball capable of smashing through droids without being deflected.

Note the underlined part: you can only receive them on certain levels. Also only on certain levels can you receive more than one as required for the achievement.

A partial list of suitable levels is given in the last section of this guide.

This is a simple list of tips. The bolded ones are the most important.

• The number of modifiers depends on the level. The type of modifiers is random.
  
• Once you find a level with at least two modifiers, play it until you know whether the two modifiers are the same. If they are, they will stay the same even if you restart the level. Try a different level in between and they might change, because that's how RNG* works (unless it works like ERROR claimed in the comments: that even restarting the level would randomize the modifiers - I urge you to try that and report your findings in the comments).
  
• If you find both of the required modifiers in the level, stay there until you can grab them in the correct order.
  
• If you miss them or get them in the wrong order, you can press Esc and Return to Tower to restart the level and try again.
  
• Remember that you can only grab the achievement in the Main game mode.
  
• If you are almost at the end, fear not! Once you finish the game (required for some other achievements anyway), you start in the beginning with all your upgrades and can play all levels again.
  
• How to be sure you got it? Achievements unlock after exiting the game. Once you think you got it, you can exit the game regularly or even by ALT+F4. If you're lucky and you did it correctly you will have one more achievement. I know this for a fact because the game froze after I got it and I had to ALT+F4 to proceed.

* RNG = Random Number Generator

If you succeed, it will look like this:

In these levels me and others have encountered two modifiers:

• Basement, level VI
  
• Basement, level VII
  
• Engine Room, level V
  
• Observatory, level IV
  
• Observatory, level V

This is not an exhaustive list. Note that all these levels have large amounts of Standard Droids. Be on a look-out for modifiers in other levels with high number of droids. They might qualify as well. If you notice this in some other levels, please post it in the comments so I can add it to the list.

It's also seems possible that the number of modifiers is random.

Remember that if you encounter both modifiers but in the wrong order, you can repeat the level any number of times and encounter them each time in some order.

If you encounter two of the same modifier, there are two possibilities:

• Exit the level and try another level in-between before returning there. This might change the modifiers. (why?) I know this because I tried it in Observatory level V and initially encountered both modifiers, then played level VII and returned to find two Fireball modifiers. The type seems to be based on RNG that rolls again when you complete a level.
  
• Restart the level and try again until you find both modifiers. ERROR suggested this - it might work and would be preferable if indeed true but I haven't confirmed it myself.

These levels are potentially also suited for the following Achievements as well, if you haven't got them yet: The Juggler, Nikola's Legacy, Gatling and Feelin' hot, hot, hot!

Hopefully I could be of service. Happy hunting!