I don't know about it being any easier to kick a diet soft drink addiction... I've known several people who were pretty addicted to Diet Coke and drank several per day.
The first two things you need to find in yourself are the willingness and the discipline required to change your mindset and your habits. It sounds like the willingness is there, but nobody can do this for you. Just like with any other habit or addiction, you have to become your own disciplinarian.
These things always take time. Don't set yourself up for failure or disappointment by trying to quit "cold turkey". That only reinforces the notion that you can't do it if you have a setback or give in to your cravings.
Start by setting realistic boundaries for yourself. These are not "goals" you hope to attain. These are BOUNDARIES you need to respect in order to be successful. Limit your soft drinks to one per day, for example, and don't feel guilty about that one per day. You're in the process.
And don't reward yourself for keeping your boundaries by binging on Mt Dew! Instead, after a week or two with no slips, do something else for yourself unrelated to this, but something healthy and rewarding. If one per day is too drastic at first, make it one in the morning & one in the afternoon...whatever. Just set some boundaries & respect them.
After week or two, move the boundary a little bit. Substitute the drinks you're taking out with a healthier alternative that you also enjoy. Water is GREAT! And believe it or not, you will learn to like it more than you think. Keep enforcing this process until you no longer crave Mt Dew every day. Eventually, you may be able to enjoy one OCCASIONALLY without feeling guilty or experiencing the negative side effects.
I used to order a Coke every time I went out to eat at a restaurant. Besides the sugar and caffiene, it was relatively expensive! I would try to drink other things, but I didn't enjoy my meal as much with a bland glass of water. I started flavoring my water with a lemon wedge & making more of an effort to drink more water and less soft drinks. Eventually, I got more accustomed to the refreshing cleanness of cold water compared to the sugary sweetness of soft drinks. I don't even like soft drinks now unless I'm drinking out of glass! I rarely drink them out of plastic bottles or aluminum cans. They just aren't as good! I usually have a soft drink with pizza or a hamburger, and it's SO GOOD! I just appreciate it more when it especially compliments the foods I really enjoy it with. Otherwise, I may have tea, milk, lemonade or even water! There are countless choices, and many you can enjoy just as much as the Mt Dew you've grown addicted to.
Good luck! These things aren't easy, but they're also not impossible. You can do this!