Betty's Gum Store is located in Popo City.
After getting off the train the next screen is the Entrance with like a little customs gate, just say your a Tourist. Head down the escalator in to the Station, down two more escalators (there's only one way really) and then you’re in Popo City. Walk 2 screens to the right and you will see a sign for Betty's Gum Store in the ground.
Jump down the hole to talk to Betty, she'll make you sign and eat (!) a contract before she can sell to you. Once youve selected the contract from your inventorty, accepted and eaten, you have to buy the following for the achievement:
Gumcore 43B - 10 smurt
Gumcore EFT99 - 160 smurt
Gumcore 56E - 168 smurt
Gumcore D341 - 1248 smurt
All well and good but you probably dont have 1586 smurt on you. Easily solved as it can all start with 22 smurt. Credit goes to "capappy" on Steamcommunity.com for this money making solution.
From Betty, jump up and out the hole and go right. Walk under the big credit sign and straight off the screen. You'll be under the tram station that says "info". Down the steps, you'll probably fall in the dumpster, then jump out and up to the green platfrom at the edge of the screen. Keep walking right, all the way along, you'll go down then up some short steps, then jump over a small gap so as to keep walking under the bridge, then over another small gap before the screen changes. You'll now be under a sign that says TSI Central with an arrow pointing to the right. If there isnt a train track in place wait for it to appear so you can jump up those light blue platforms on the far right next to the signs pointing up saying Central. Walk right then get sucked up the pipe. Walk right straight throught the next screen with the big statue and it's the screen after that we are looking for.
You should see a little snack truck with a rednumber above it. This guy sells Fried Smackmoffel for 22 smurt. Buy however many you can afford. Even if it's only one. When you can't afford any more, take a left in to the statue screen, jump up on the statue platform and into the pipe with the two signs pointing at it (first pipe of the two left pipes). You'll shoot out of the top of the pipe after a few second and you need to go left. On the next screen will be a Store with a pink sign, just below you. Jump down to this matey and sell the Smackmoffel for 45 smurt, doubling your money. With the profit, go back to the snack truck to the right of the statue screen and buy more smackmoffel. Rinse and repeat untill you have lots of money, then go back to Betty's Gum Store to buy those four weapon add ons and get your achievement. It took about 10 seconds for my achievement to pop.