It’s a shame DC Comics didn’t go all the way here. From one of the panels it seems the Penguin has survived being shot in the head by Red Hood. Not sure what kind of a marksman he is if he can miss at that close range.
From – Red Hood and the Outlaws Vol. 2 #24
It’s probably a double play like Red pulled on Bats in the first issue. Still shot him but making him brain dead or something. There’s no way DC would get rid of the Penguin.