Possible Solution:
1. Rxa5
2. Bxc7
3. Nxf1
4. Rxf7
5. Qxe5
6. Bxc3
7. Nxg5
8. Bxe7
9. Nxg6
10. gxg7
11. gxg8
12. Rxa8
13. Qxh1
14. Qxh8
Method:
Started by finding what moves were possible from the start. Then looked to find areas where a piece could only capture one piece to narrow down chunks of moves. Tested through possible routes.