Getting out of this debt is possible. It just takes some determination, planning and self-restraint.
Unfortunately I cannot suggest ways to improve your credit score quickly.
Here are some suggestions to help you get out of debt:
Definitely avoid minimum payments as much as possible. Rechu is correct. Instead determine a higher but affordable monthly payment.
Determine which card will be your main one and only use that card. Cancel the other cards once they are paid off (especially the store variety).
You could try making a monthly budget and allocate a certain amount of funds for each week. Anything left over at the end of each week can be put aside. At the end of the month this extra money can be put towards your debt.
Finally, avoid impulse purchases as much as possible.
Good luck.