I read this somewhere in the late 1980s to the early 1990s, in black-and-white, maybe as part of a coloring book/activity book. Batman and Robin confront The Penguin and one of them is shot in the chest. I remember that the panel show the shot as being a fluid erupting from the umbrella's tip, but in retrospect, that might have been intended to be smoke, or my young brain (I was probably about 6-10 at the time) reversed the direction of things. What does stick out in my head was that the bad guy got away, after which the member of the duo who was not shot noted that they would be unable to get to a hospital before a storm (tropical storm? Hurricane?) hit, so they bandaged up the wound and tied both of them down (I think to a palm tree) to wait out the storm, with the final bit in the story having the one who was shot exiting the hospital with a bandaged torso, but alive and well.
In retrospect, I'm not 100% which one of them got shot... both make sense in my head, with the other tying them down during the storm, then getting them to a hospital. And it's possible that it might have been The Joker using The Penguin's umbrella. I have another vivid image of my head, possibly from another page in the book, with The Joker operating a drum set with a snub-nosed revolver hanging off one of the pins on the bass drum.