Aquatic planets contain mostly water with lots of underground terrain. Within the caves you are able to move in any direction.
To go deeper into aquatic planets, you have to upgrade your Plating. If you go deeper and pressure rises above what you can sustain, you start taking damage. Go back up or repair the damage before dying of low health.
To stay underwater you also need oxygen, but no fuel. Small amounts of Oxygen appear as gas bubbles floating up from patches of see gras. If you're near them you will collect them for a tiny refill.
Available materials: Edit
see also Base_Elements#Quick_Reference_Chart
|Plasma (from Geysers)||0-150m|
|Unstable Isotopes (from Oxygen)||150-250m|