When the base is hit, Henry appears as the boss. Three Shy Boys pop out with about 15 seconds between each one and they are at a high strength magnification of 2000%. The Doge Dark spam is now more effective due to a bigger enemy limit.
Meatshields, very good combos and Cyborg can do it easily, better if you add a good anti-red or anti-floating cat such as an uber that is good for these situations or Cameraman.
Keep in mind that there's plenty of money, so go with spammable cats rather than cost efficient ones (In other words, no Bath Cat), a stack of Cyborgs can make quick work of the Doge Darks like they were simple Doges.