Just to be clear, this isn't some bullshit where "circles don't actually have edges harharhar" right? My preemptive answer: 1) Choose one direction/point at the edge, and "draw" a line, from you at the center, to that edge. 2) proceed to go in circles relative to the centerpoint, but in a spiral motion so that your completed revolution is at a point slightly further down the line each time. This forces the monster to constantly go in circles while you move infinitely closer to the edge of the circle. 3) You will eventually be on a point infinitely close to the edge of the circle, i.e. the shore, wherein touching the shore doesn't pass any actual time for the monster to be able to be allowed to move to your position. 4)?????? 5) Profit
Turns out I told it correctly: https://puzzling.stackexchange.com/questions/2155/the-lake-monster wasoxygen found it on StackExchange.
Wow, okay, so I didn't even tell the question right but you still got the answer. The gist of it, I think, is that you can row 1 radius and the monster can run 4r and so you need to "shorten the circle" by rowing to r/4, whereupon you can move around the circle faster than the monster can run. I believe. That was roughly my solution (after I sugged 8bit's everlasting spiral) and my friend said I got it, but I may be mixing up the details. I'll try to get back to you with the actual question.