This enemy is the Goliath to your David. He has incredibly high health and attack (though, oddly, not as much as the much smaller Manic Eraser), and a 1-in-4 chance, with every attack, to do a massive, extremely deadly Wave Attack. This attack will kill most Cats, and the extremely lucky survivors will be low on health or slowed for a long time.
You can stall him just like your own Crazed Titan Cat, by making it miss. The Gory Blacks that spawn in groups help you accomplish this by eliminating your meatshields that Manic Jameira would have attacked, as if an enemy misses their initial attack, the wave won't happen.
Using Octopus Cat or Cat Machine Mk3 to negate Jamiera's Wave Attack will not guarantee that your ranged attackers will survive. Because of Jamiera's sheer damage and the units' inability to outrange the boss, Octopus will only be able to block the wave within a small window, and Cat Machine's survivability depends on if Manic Jamiera slows him or not. Also be wary that if the boss creates a wave on the same hit that your wave blocker dies, they will not block it, and every unit behind will get destroyed.
The only wave blockers in the game to break this rule are Eva Unit-00, Hatsune Miku: MM2020 Tokyo and Mighty Kristul Muu since they have 350, 350 and 400 range respectively and can outrange the boss, who only has 320 range. If you have any of these quite rare units, this enemy is turned into a complete joke, as all of his wave attacks are negated, and they can outrange it. This means that you are able to stack cats that would normally not be a good idea to use, such as Lufalan Pasalan.