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 animation 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 should be broken as late as possible so as to avoid knocking him back.
Due to how it works, he will likely never advance after stopping for an attack (Unless you get Kubilan or the cannon involved, which would be a dumb thing to do), 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 3 ways are the following:
stop him close to the enemy base, push him behind and forget about him completely (only usable if he's not set as boss, of course).
Just use an army focused on many medium-small units and replace them upon death, in all his COTC appearencec this is a valuable strat.
use wave blockers; MK3 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.