This requires you to get $100 Billion funding.
It sounds hard, but it's mostly a time sink. Set up lots of rare metal extractors (be sure you've deep scanned everything too) and have them run.
Doing the Launch SETI Satellite special project can help too, as does tourism.
A Space Elevator is also key to this since it can export 100 Rare Metals at once (and doesn't have a travel time).
Having a sponsor that pays a lot for Rare Metals would be good too, but isn't required.