Batman's superpower is that he's always got the EXACTLY RIGHT piece of equipment for THIS PRECISE SITUATION. Falling off a building? Grappling hook. However, the stipulations would be that 6) it can't kill anyone and 7) it's gotta be bat-themed. I'd just give him TWO supernatural dice, like a d6 and a d8, along with 1d8 skill. I suppose Batman's a good candidate for 1d10 armor
Here's a batman-specific crash course in brikwars superpowers: Batman has a d8 and a d6 held in reserve as his "superpowers." whenever you need him to have something, just make something up and use the two dice as the variables you need. You could, for instance, make a field of bat-caltrops 1d8" in diameter, that does 1d6 damage to anyone who steps into them. For as long as that field existed, Batman would be unable to access his dice. If Batman preferred to hold onto his dice, he could instead use them to boost himself with his own super bat-speed of running another 1d6" because he's The Goddamn Batman. His 1d6 supernatural die would be ready again to enhance something else. You could even use the d8 or d6 to re-roll (but not add to) a skill roll!
For the Ninjago Turtles, you could easily apply a supernatural die to all of them and use it explicitly for kung-fu. I think you might already have some ideas by now for examples,so I'll let you just go with it.
If you're combining a supernatural die into an action (or leaving them out for an extended period) you'll also have to suffer a -1 distraction to skill rolls until they're returned to you (at the beginning of your next turn). If you need point or fire an ability at a specific spot, that also requires an action. Otherwise, however you're thinking it in your head is probably correct.