Benax is very strong here and will probably defeat both of the first two dogs on its own, leaving your remaining two pets to leisurely clean up. I used Gulp Froglet for this, but nearly any Aquatic pet should work. You probably won't even bring the third pet out.
TD script courtesy of Thordros#1784.
Based on the comments below, Mud Jumper (suggested alternative to Benax) may sometimes work but may require some improvisation and more careful selection of your second and third pet. Your results may vary. Benax is guaranteed-- Mud Jumper is not.
The strategy offers a TD script that can be used with the TD Script addon. You can copy the script by clicking on the button to the left of the pets.
This strategy is impacted by changes to pet battles made in patch 8.3. The strategy might not work properly anymore and needs to be reviewed.