If you don't want to catch monsters, then only fight the fishing stamina if you get a negative comment. When you get a positive comment like "You have a good feeling about this!" then its a monster.
In addition to Levitz' comment: You can reel in the tuna, which check as "terrible feeling," without line/rod breaks
(setup: Fishing 33 with composite + sink minnow @ ferry). However, there were times when I lost my catch after depleting the fish's HP completely. n_n;;
I usually fish this on the Selbina <-> Mhaura ferry with a minnow. It will also pull up cone calamary, bluetail and noble lady which all sell for a moderate price.
As Levitz said, the tuna will be the (!!!) with negative comments.