Adrian,
Note that you can still use shutter priority (S) and achieve what you want. As you are using a 90mm lens, the rule of thumb for shutter speed for handheld is one over the focal length. i.e. in theory you should be able to shoot at 1/90s. That assumes good handheld technique, so perhaps you should go for 1/200s (which should be more than enough based on the Exif of the first 3 shots you posted).
The last 4 you posted look pretty good, but you still have the lens wide open. This will give you almost no depth of field and also won't be in the sweet spot of the lens. Most macro lenses have a sweet spot somewhere between f/11 and f/16.
Another problem with shooting macro handheld is keeping focus. Unless you can hold the lens perfectly still, there's a good chance that what was in focus just before you pressed the shutter won't be in focus when the shutter is pressed. This is mainly because of the very narrow depth of field in macro shots (even with smaller apertures). When using a tripod (or even a monopod), you have much more stability and it is easier to both focus and keep the focus, especially while pressing the shutter.
Be aware that while shooting into an aquarium you are shooting from a medium with one optical density (air), through another medium with a different optical density (glass) to another medium with yet another optical density (water). This means that if you don't shoot perpendicular to the glass, you'll get refraction. The further off perpendicular you go, the greater the refraction and the more distorted the image will be. I say this because you say you found the tripod does not give you a good angle. While you may be able to get a "better" angle with respect to the scene without the tripod, you may be introducing distortion into the image.
Off topic, but that
Acropora on my site was taken at a depth of nearly 30 metres, which just goes to show that the claim of many aquarists that
Acropora require high intensity lighting is bogus.