How can Valonia ventricosa cells get so big?
Ventricaria ventricosa (previously called Valonia ventricosa) is not exactly a single cell. It has a coenocytic structure with multiple nuclei and chloroplasts. As Jasand Pruski correctly guessed the organism possesses a large central vacuole which is multilobular in structure (lobules radiating from a central spheroid region). 

The entire cell contains several "cytoplasmic domains" with each domain having a nucleus and a few chloroplasts (See the figure below). Cytoplasmic domains are interconnected by cytoplasmic "bridges" that are supported by microtubules (like in axons). The peripheral cytoplasm (whose membrane is overlaid by the cell wall), is only about 40nm thick.

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  Fluorescent confocal micrograph of a cytoplasmic domain. From Shepherd et al. (2004) Protoplasma 223: 79–91. Here, n is nucleus c is chloroplast and v is vacuole.


So these are not huge cellular balloons that can burst easily. Nonetheless a huge structure like this is susceptible to injuries by shearing forces of water currents and by other organisms like fish which may try to feed on them. These organisms have some mechanisms other than the cytoplasmic organization that allows them to cope up with injuries:


When the outer membrane ruptures, then the cytoplasm contracts with the help of actin filaments that are attached to the former. Subsequently the membrane fuses, protoplasts form and then cell wall is regenerated. This movement is likely to be triggered by extracellular calcium.
A single cytoplasmic domain with nucleus and other essential organelles can regenerate an entire organism. 
A muclilagenous layer made up of sulphated polysaccharides coats both the vacuolar and extracellular surfaces. During injury it impedes the movement of water and ions (by retaining them in the form of a gel) and therefore acts like a plug.


Other organisms like this (siphonous algae) also have similar mechanisms. Some even employ calcium carbonate to maintain rigidity.

REFERENCES:


Shepherd et al. (2004) Protoplasma 223: 79–91
Menzel (1988) Protoplasma 144: 73-91