Combine diced tomatoes, chili beans, black beans, corn, beer, and tomato sauce in a slow cooker. Stir in onion, carrot, and taco seasoning until blended. Place chicken breasts on top of the mixture, pressing down on each one to slightly submerge. Cover and cook on Low for 5 hours.

Remove chicken breasts from the slow cooker and set on a cutting board to cool slightly, about 10 minutes. Shred meat and return to the slow cooker. Cover and cook on Low for 2 more hours.

Ladle soup into bowls and garnish with Cheddar cheese, cilantro, sour cream, and crushed tortilla chips.