After trying many unsuccessful attempts at this, it finally happened by chance or design.
Enter Arcade Mode and hope to get lucky. This achievement is somewhat luck based, but you can increase your chances by doing the following:
The best advice I have is to wait for banana powerups, preferably Freeze (the light blue/grayish one) BEFORE you start slicing fruit, and wait until it is almost off the screen. This keeps your score low, and possibly makes powerups more frequent. Once Freeze is going, just keep a watchout for a second powerup. Wait until the freeze has nearly ended, then slice that banana powerup. This will lengthen the freeze time combined with the second powerup, and it gives you the best chance for that lucky third banana powerup to appear.
I read the comments and other solutions before I tried my method listed here. It may not work for everyone, but after hours of frustration, hopefully this will help someone. :)
Good luck, and happy slicing. FYI, it took me over 25K fruit sliced before the first Triple Stack ever happened. If this helped you, up me; if not, tell me so I can improve it. Remember patience, grasshopper...
EDIT: Some gamers have also mentioned that waiting until the game is almost over may not increase your chances of getting all three, but that is what worked for me.
Tip from Hamfam9598 - You should wait to slice the first banana powerup until it is almost off the screen. The other two you can slice right away when they appear.
(Let me know if anything is unclear instead of neg-voting and I will edit this as needed)