I go this by accident so you might get it the same way. At the time the achievement unlocked I had multiple fish from 3 different species all hanging around my hook and trying to bite it. I kept tapping
to move the hook away from the fish I was trying to avoid catching and this generated enough interest to attract 5 at once (the achievement unlocked for me without having any fish on my hook). I can't remember where I was and what my exact setup was at the time but what I do remember is that all of the fish were Small in size and I was fishing with one of the hooks that defaults to sinking to the bottom but can be made to float freely by just reeling the line in. My hook was near the surface at the time but I doubt that matters. I expect that having enough fish available and keeping enough of them "in play" by tapping
is what mattered.