Yep, patience is the key. I just kept telling myself that trying to eat the big ones quickly would only save me a minute or two, but getting eaten would cost all the time I already put in.
Ultimately, you will get big enough to fill the screen.
Geez! I got to 85,000 and the end of the eco system, but it took me like an hour and a half!!! After a while, you can just leave the fish in the middle of the screen and go have dinner.