Destroying all the credit card data centers

in order to wipe out people's credit card debt. If you destroyed enough data centers, you could erase all records of credit card debt
Visa's main data center is a fortress with a moat built to withstand hurricanes and earthquakes. It would take a bit more than a homemade bomb driven into a parking garage to bring it down. linklink
Unfortunately Too many backups and contingencies exist for the sole purpose of data recovery these days. If you did this 100 or 150 years ago? Absolutely.
Today it would take wiping out every server farm (which are likely off site), every offshore location (more backups), and the government in order to "erase" your debt without paying it off or filing bankruptcy.
Yet Project Mayhem wasn't only happening in the one place. It was actually a nationwide thing. So assuming that the correct buildings were blown up across the country, then I can see PM being a success.
The FDIC would get all the relevant information to resolve the issue and transfer the rights of debt over to new parties (or back to the credit company, just at a different office, such as a branch office)
FDIC is an organisation, not just a single building. They have branch offices like many organisations have multiple offices. The main office is in Washington DC, but they also have offices in Atlanta, Boston, Chicago, Dallas, Kansas City, Memphis, New York City, San Francisco, and a satellite office in Arlington, Virginia (this office is mainly for support roles).
Assuming we somehow blew up all of these buildings, there would still be employees who were either off of work at the time or retired. Retired officials would be asked to come back to work to provide assistance whilst the FDIC is rebuilt.
Assuming we killed every member of the FDIC whom is alive, there is still the issue of the government has charters over the roles and responsibilities of the FDIC. The government would call in economists to forecast damages and the cost of repair, delegate workers from some departments (e.g. the FTC, SEC, IRS, etc.) to begin work for the newly forming FDIC, high ranking officials to ensure that agents are getting the proper education necessary for their new tasks, then they'd go back to work. They'd set up separate governmental buildings or ask /demand certain buildings allow them to be used as a temporary FDIC office 'til a new, permanent foundation can be acquired, and so forth.
Because the US is a huge asset to the world economy, many nations would also provide resources and support to ensure we get everything taken care of, so as to not damage the global economy and screw everything over. Top economists would be providing support with or without pay (up to them, I would suppose) to ensure we can rebuild without screwing up the economy should issues arise.
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 da