There is no specific "RB Bat" pet; however, the term likely stems from two popular topics often searched together:
Located near the hot springs and the Baby Shop. The Final Objective:
Enter the castle, go to the upper floor, and use the trampolines/jump pads outside to reach the very top. Adopt Me Script – Complete The Challenge RB Bat...
Located on the grey cement bridge leading toward the castle. Blue Crystal: Found near the campsite and the red bridge.
Stand near each crystal until it glows, indicating it has been collected. There is no specific "RB Bat" pet; however,
Touch the RB Battles Trophy at the peak to receive the badge and a limited-time pet wear item. Clarification on the "RB Bat"
Use a flying pet or ride the hot air balloon (which costs 5 Bucks) to reach the Sky Castle. Blue Crystal: Found near the campsite and the red bridge
To "Complete The Challenge," players had to locate and activate three hidden crystals (sometimes called totems) across the main map of Adoption Island: