Hi James, welcome! :)
This can be quite a common fault with remapped cars, as the increased torque causes the clutch plate to slip.
You will not NEED a new dual mass flywheel, but many people recommend fitting one at the same time to save on labour if it goes later, though this will add significantly to the parts cost.
The only bit causing the slipping will be the clutch assembly itself.
If you're handy with a spanner etc, the cheapest method would be to do it yourself minus the DMF. Not too sure on costs I'm afraid, will depend on the exact model you have. Also, if you go to an Audi dealer the labour plus parts will cost a small fortune if you include the DMF.