Definitely don't have the camera do any image correction. You want to get the unchanged original image off the camera, save a copy, and do all image correction using good software.
All image correction should be done by eye. The best software can only do some basic things. It can't really react to things like your underwater photos.
Normal pictures are very quick to correct but yours has distorted color from being underwater which takes a little more work. You have to go into color balance and get rid of some of the green and yellow.
If you're really trying to take good pics you need to take pics of a color checker card along with your photos. You do the color balance on the picture of the card, save the settings, then apply them to your other pics.
First thing to check and correct on pics is the levels (photoshop's term). In Lightroom I believe it's Histogram. You want to get rid of the low or empty area. Below is your picture's levels. You see how I slid the right arrow to the left where there's no info - it's really low or nothing:
That is the first thing to do with all pics that have low areas like that. After that, I did the color correction which is too much to show. It took only one minute literally. You can look up help on it. The other corrections were raising both the Saturation and Contrast and then using Curves to darken a little. There are other ways to darken.
Here's your original image:
This is your preview image:
Here's your original pic processed by eye:
You can see how you're in control of the color. If you use a color card you can totally remove the water which I don't know if you want to do. I think I should have left a touch more green and yellow in.
