Nichrome used for heating is usually welded, not soldered, because the operating temperature is usually above solder melting point. However, if the solder joint is well heat sunk by the copper side of the joint, you might be able to use a high melting temperature solder.
Once the nichrome has been red hot for some time, it forms a very tough oxide coating that makes either welding or soldering very difficult unless the oxide is removed.
I would try cleaning one surface with very fine silicon carbide sand paper (600 grit or finer) and silver solder with silver solder flux. This will require the heat of a butane or propane torch. If you don't require the temperature capability of silver solder, you can tin the nichrome with it, and then use low temperature tin lead solder to attach that surface to copper.