How can I avoid fungus in an alien water tank?
It looks like you're making something rather like a specimen in a jar, so why not do it the way the professionals do it: pure ethanol or isopropyl alcohol?

As long as the jar is properly sealed, this should keep your alien fluid in pristine condition for centuries to come.

Of course, this may be overkill. If you do a decent job of sterilising the jar beforehand (I recommend the kind of steriliser used for brewing), boil the water beforehand and seal the jar properly, then even without additions the inside of the jar should stay bacteria/fungi/mould/algae free for months or years.