The Nail Bat can be earned in Chapter 8 after completing Kids on Patrol.
The Nail Bat for Cloud is all about health and critical hits, but comes without hardware slots before upgrading. His ability, Disorder, allows Cloud to launch a devastating attack that will switch him between positions. To learn Disorder faster, all you need to do is attack an enemy with a regular or strong attack after changing position.
To complete Kids on Patrol, you must first reach the slums in Sector 5 with Aerith, and find the two missing children. Once you've done that, you'll unlock side quests for the region and can return to the Leaf Orphanage to start this one.
The five missing children are scattered around the slums and are fairly easy to find. They all have a wooden Buster sword on their backs and a shiny green icon above their heads. Once you find the five children, they will eventually ask you to defeat the Toad King, which Cloud agrees to do for 3 gil (such a nice guy).
Head back to the area where you found the two missing children for the main storyline earlier (Toad Marsh), and there you will find the King. He is a rare Hedgehog Pie and will have two regularly with him. Like the others, he is weak for ice magic, but he will protect himself or his compatriots.
Don't attack the protected target: you'll do virtually no damage and they'll bounce off your face (literally). Focus on the softer targets and hit them with Blizzard (Aerith's Arcane Ward is perfect for this, so give him the Ice Materia).
Once the king is dead, return to the Leaf Orphanage and receive your brand new Nail Bait.
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