The phrase "big attitude" is an idiomatic expression that means having a large or significant amount of confidence, self-assurance, and assertiveness. Full definition
This team provides treatment for fearful dogs, small dogs with big attitudes, dogs with resource guarding issues and those who are reactive to other dogs. (kyhumane.org)
A little dinosaur with a big mouth and even bigger attitude awaits you in Kodansha's release of Gon (Vol.03). (otakuusamagazine.com)