Short answer: try increasing the ISO rating to 400 or more; get close to the subject; illuminate the target, or focus on something next to the target.
Long answer:
If the blur seems to be caused by motion (of the fish or you) then you probably need to use a faster shutter speed. A shutter speed of 1/60 sec or faster is probably needed to `freeze' the motion. To control the shutter speed you could switch to shutter priority ('S' or 'Tv') where you set the shutter speed and the camera works out the aperture. Or you could set it to manual ('M') where you control everything.
You can also influence this through the ISO rating. If the ISO is low (50 or 100) then in a dark scene there may simply not be enough light to get a decent photo in 1/60th of a second. To avoid that problem we could increase the ISO sensitivity to 400 or even higher. If 1/30 second at f/4 gives a decent exposure with ISO 100, then 1/60 sec at f/4 gives an equivalent decent exposure with ISO 200, and 1/125 sec at f/4 at ISO 400 is the same.
Anyway, if you just dial up a higher ISO rating, even the point-and-shoot 'P' mode should yield better pictures.
Autofocus on compact cameras is a pain. In low light they do not perform well. To get faster focus on a target, try illuminating it with your torch. Alternatively, find something with good contrast that is near the target, focus on that, then hold the focus and point at the subject. Oder, focus on something with good contrast that is in front of the subject, hold the focus, move the camera slightly forward, and shoot. etc. 'Good contrast' means a sharp boundary between light and dark, and enough light overall. Many of the autofocus detectors look for a sharp change in brightness in a particular direction (a vertical edge or a horizontal edge) .
Shutter lag cannot be helped. Although I find that shouting "aaaarrrrrrggggghhhh" will help scare away all the fish so that you do not become upset at being unable to photograph things... My buddy calls it "camera rage".
To be more precise: what cannot be reduced is the delay between (1) the time when you have achieved focus with the shutter button depressed half-way and then press the shutter button down fully, and (2) the time when the picture is taken. That is a fraction of a second.
Most of the delay is in the autofocus. You can avoid that delay by anticipating the motion of the subject. For example suppose your fish is going to pop its head out of a hole eventually. Focus on the hole itself; hold the focus and pull the camera back a tiny bit so that the fish will be in focus when it does pop its head out; wait for the fish to appear; and fire. Works for me
HTH