Although Axoloty has a relatively long attack animation and can even miss at times, his attacks are devastating, with a 100% chance of creating a Lv.10 Shockwave. Much like Zamboney Cat, however, Axoloty's backswing is so long that he will rarely (if ever) attack more than once. Note that if Axoloty gets knocked back, he will immediately start another attack, making the default Cat Cannon a poor choice against him. He also has a Barrier with 10,000 HP, which can help to avoid knocking him back.
Due to how he works, he will likely never advance after stopping for an attack, for this reason, it is recommended to stop him ASAP, to give you time to recover after every attack he does.
As to how you avoid his attacks, the best options are as follows:
Stop him close to the enemy base, push him behind and forget about him completely (only usable if he's not set as a boss, of course).
Just use an army focused on many medium-small units and replace them upon death, in all his CotC appearances this is a viable strategy.
Use Wave Shields; Cat Machine Mk 3 can tank the hits, while the others need timing, but it's doable, you only need to keep in mind that whoever gets hit by the regular attack will likely not survive.
Killing him quickly and stun-locking him are also good strategies if you have the right condition and right units.
A space salamander with a Cat allergy. The powerful winds of its relentless sneezes are [sic] should be avoided by small Cats who could be blown into another dimension.