There are a few ways this could (theoretically, with almost 0 probability of success) be done:
Go forward by generating new private keys until you find one that corresponds to this address. There are about 2^256 possible private keys (actually a smaller number, but it's huge).
Go backwards by breaking all the cryptography involved in Bitcoin:
First, that address is the hash 9f03f344848612f1f456b08187706017888a6bb6. This is in form hash160, which is
RIPEMD-160 (SHA-256 (Public Key)).
Step 1: Break RIPEMD-160 to get the SHA-256 hash.
Step 2: Break SHA-256 to get the public key.
(You could also get this public key once it's published when that key is used to spend. Of course, at that point it may not help you.)
Step 3: Break secp256k1, Bitcoin's elliptic curve, to get the private key from the public key.
Good luck spending less in research costs than the $4,500 you hope to get back. (Plus if you somehow succeed, consider the greater impact on Bitcoin.)
- Determine who owns the address and get the private key from them.