Hi Doris,
I'm sorry to hear about your achilles, but at least once the area is healed, you should be feeling much better.
Even though you can't place weight on that foot for one month, continuing with upper body exercises (check out the strength training exercises recommended on this site) will indeed help you to burn calories and fat and lose weight. The more lean muscle mass you have, the more you burn - all throughout the day.
You may still be able to try swimming and aquatic exercises because you are boyant in the water and not placing any great pressure on your feet, but it depends on your situation and if you cannot get the area wet.
In addition to swimming, you can also try the upper body ergometer, in which you only use your upper body to perform the cardio.
Of course check with doctor on all of these things. Start slowly and stop if you feel any pain.
Let me know if you have any questions.
Good Luck,
Paul