Well exercise is great. Try to mix up your workouts with some cardio and some weight training. Hitting all the major muscles will help to tone and strengthen those muscles (Making the swimsuit look better) and will also help burn more calories per day on their own.
Also look at estabilishing a realistic diet. Exercise combined with some good diets can yeild about 1lb a week. You'd loose about 8lbs in 8 weeks and thats more realistic than 20lbs.
I'm guessing your a woman based on how you wrote what you wrote, and i'd say 1800 calories is probably the least you want to eat a day.
Check out fitday.com (its free) and start putting in what you eat each day. It will help track what your eating calorie and nutrient wise. From there shoot for that 1800 calorie per day. Anything less than 1500 will put you into starvation mode and you'll end up causing more issues than you want to know.
If you did weights/cardio/weights/cardio/weights for the week you'll find you do a few things well. 1st Strengthing/toning/burning calories with working out. 2nd Cardio helps get the blood to those muscles you used, and helps to recover them quicker. So your doing a 1-2 knockout on a good workout schedule.
Focus on the core muscles vs trying to 'target' small ones (like arms).
Do things like Pushups, pull ups, squats, lunges, crunches (on a ball is good or declined). These core exercises will work a large variety of muscles and help build an over base, core and upper body
Good luck and keep us updated on your progress
