These attacks are really hard to defend against because the attacker uses automated "bots" that are capable of subscribing an email address to multiple email lists per second. Here are a few things that might help:
Enable the Bulk Mail Filter
The Bulk Mail Filter will prevent most subscription based emails from reaching your inbox. If there are any newsletters that you do want to receive, you will need to add them to your Approved Senders list. Go to Settings > filtering policies and select the Bulk mail filter option to enable this feature.
Block the senders
In the case of subscription bombs, usually the senders are not intentionally spamming since they are just responding to a subscription request. Because of this, reporting the messages as spam is not recommended since our spam filter requires multiple accounts to report a message as spam before a rule is created to block it. Instead, it is recommended that you either unsubscribe from the senders' messages or block the senders. Senders can be blocked by hovering over the message in the Quarantine+ > Clean mail view and clicking on the Block sender option.
Create Custom Filters
While enabling our bulk filter will block most newsletters, the initial confirmation emails that most mailing lists send upon subscribing can still create a pretty big mail bomb. One way to at least reduce these emails would be to set up some custom filters that block emails that contain the word "confirm" "confirmation" or "subscription". Custom rules like this can be created by going to Settings > custom filters. Of course, there would definitely be a trade off for creating these rules because then any valid emails that contain these words would also be blocked.
Change your online passwords
You may also want to make sure all of your online accounts are secure as there have been reports in the past that hackers use subscription attacks to bury emails from institutions like Banks, PayPal, Amazon or other sites so that you won't notice unauthorized withdrawals or purchases. A recent report noted that scammers will go as far as use the "archive" feature of Amazon to hide unauthorized purchases on your Amazon account.