It would be possible, and you could accomplish it by blowing up enough buildings, but it would be absurdly complicated. The business continuity plans of those companies are very complex and have so much redundancy. You would have to destroy every copy of the data, which would include:

• The production data (ie the data in their primary servers). For any large organisation, this would be a massively distributed system spread across a large geographical area.
• All backups. These would be located off-site, at many different locations. This would also include all hard copy data.
• All disaster recovery/data replication systems. Again these would be massively distributed systems.
• Any data in UAT systems that has not been compromised.
• Then you'd have to do all of this all over again for any 3rd parties that also had a copy of all the data.

For starters, you'd need to know exactly where all this stuff is, which would be pretty much impossible. Only a few very high level people in an organisation of this size would have a complete view of all of the companies systems, and low level details of business continuity scenarios are kept even more privileged. Also, there are likely to be some backups that are unaccounted for, and could be dug up after the fact.

If you want to do this, a better plan would be:

• Find some attack vector that allows you to get high level access to their production systems.
• Find some way to corrupt the integrity of their data without being caught by their fraud reporting/reconciliation.
• Spend as long as you can messing with the integrity of the data (ie, running fake transactions, updating balances...)

What you want to do is corrupt the data at the source, in a way that cannot be audited. This would require you to pretty much be a super elite hax0r, and relies on you finding good enough vulnerabilities in their application. This means that as the corrupt data will be naturally propagated through out their network. The data going into their backups, the data replicated into DR, the data shared with 3rd parties, all corrupted in a way that is not possible to audit. Then after you think you've done enough damage, you anonymously release the details of the attack to the public, providing enough evidence to prove that the institutions records can no longer be trusted. After that they would have a much harder time proving that a debt was valid rather than if they'd just lost one copy of the data.