You will need a pretty large amount of coins for this achievement since it requires you to purchase all upgrades. The only 4 things you need to buy for this achievement are listed under the Upgrades section (highlighted in blue in the shop that you can visit before starting any level). I will list them here along with how many coins are needed to buy the last slot of each category (Sorry, I didn't keep track of each slot but if someone wants to contribute that information, please let me know and I will add it to the solution and credit you). The last slots cost a lot more than the others though.
Extra Life: (Last slot costs 100,000)
Fireball Size: (Last slot costs 200,000)
Rebounds: (Last slot costs 180,000)
Fire Wall Length: (Last slot costs 120,000)
This may seem like a very long grind but my following method will save you from wasting way more time than needed and it will also save you from purchasing loads of microsoft points (which you can use to buy packs of coins). Remember, the name of the game is not Money Burner so save your microsoft points and read ahead if you want to know the much cheaper alternative!
Luckily, the popular date/time trick used in several other Windows Phone games works wonders in this game and will be the key to getting loads of coins efficiently and for free. Well first let me mention that personally, I only spent 160 MS pts total to complete this game and I recommend you to do the following. The only thing you should buy is the Double Coins Magic Pouch which is the only Utility in the shop. It grants you 2x coins permanently! You can complete the game without spending a single microsoft point but the grind will take you twice as long (even with the date/time trick). Anyway, more on that now...
For the date/time trick, you will need to go to your phone settings and then choose "date+time". Turn OFF the option that says "set automatically". The only thing you're concerned about is the date so change that to 6/3/2013. I noticed that there are different Gold Rush setups for different weeks and after trying many (if not all) of them, I found this day/week's to be the most productive for accumulating coins. You can get around 5,000 coins from it or better yet, around 10,000 if you bought that double coin perk I mentioned earlier. Anyway, once you complete the Gold Rush for that day it will say you can play again in 6 hours but using the date trick you don't need to wait. Simply go back to the date+time screen and change the day to 6/4/2013. Go back to game and you can play the Gold Rush again! Rinse and repeat changing each day to the next one until 6/8/2013 which is Saturday. Since the next day Sunday is a new week, it will be a different Gold Rush and we don't want that. Therefore, what you need to do is set it to 6/1/2013 and go back in the game. Don't do this Gold Rush either though. Now change it back to 6/3/2013 again and you can repeat this cycle as much as you want. Another good thing to note to make it even quicker is that you can actually have the date+time screen and the game screen both open in the background at the same time and change days without having to relaunch the game! Last but not least, I will explain how to do well in the Gold Rush level itself to give you strategies for maximum coin potential...
Gold Rush Strategies
From the main menu, select the Gold Rush mode. As you play this mode there's no point in saving the coins you earn so start upgrading! I recommend first buying some rebound slots and then a larger fireball slot. In fact, don't bother with the extra life or fire wall size upgrades until after filling the other two categories since those are way more important for coin potential.
What you want to do is let the enemies get down to almost the bottom of the screen and then hold finger on screen to charge up fireball and swipe slightly diagonally left or right. This will cause the fireball to rebound off the walls and get tons of enemies in a big combo. When you do big combos, the enemies drop more coins (and higher value coins) which you need to tap on to collect. Sometimes, you will see a special green coin. If you tap this one repeatedly before it goes off screen you will get a massive amount of coins.
Lastly, at the end of the level there are various stats shown but I don't know for sure if any of the score or stat bonuses actually add extra coins to your total. Anyway, if you follow these strategies on the 6/3/2013 Gold Rush (or any other day that week since they're the same) you will get around 5,000 coins every time (or around 10,000 if you purchased the Double Coins Magic Pouch for 160 microsoft points.
Once you fill/purchase all upgrade slots (a filled/purchased upgrade slot is marked by a blue gem) the achievement will unlock!
NOTE: You may want to change the date back to normal before you unlock this or any other achievement because there is a chance that the achievement will only show up on your gamercard on xbox.com on that actual date. Use this solution to rack up enough coins for the upgrades but change date back before you actually buy the last slot and unlock the achievement.