The Batman series had a lot of lame or silly stories in the late 50s/early 60s, but the story in Detective 241 (March 1937), while seeming like a silly take for most of it, actually comes to a decent resolution, by Edmond Hamilton and Sheldon Moldoff.
For reasons that are far from clear, Batman suddenly starts wearing colourful costumes, starting with a red one, and then a blue, then green. Robin stays in his familiar garb.
Batman branches out from monochromatic outfits, with a white outfit with a big black bullseye that he wears to an archery match at which he expects criminals. It seems like a dumb costume to wear to such an event, but after the bad guys shoot at him, we discover he is wearing metal plating under the target.
And that notion would be kept in later stories, that the area directly under the bat symbol on his chest is the most padded part of the costume, because it serves as a target, and as such a distraction from shooting him in the head.
The eye-watering rainbow costume that he wears for the conclusion will live in infamy, but it served its purpose. Dick Grayson had publicly injured his arm, and the entire point of the costumes was to distract the public from Robin, and make them not notice that one of his arms was not being used. Flipping back through the story, one can see that they played fair, that one of Robin’s arms is always concealed. So it works on the reader as well as it works on the public.