We have 2 goldfish in a 13 ltr tank.Now(afer purchasing) i have heard that goldfish can be quite dirty but the tank just doesn't seem to be clean.

We do the usual 25 per cent change every week and have 2 snails to clean the algae but the tank still looks mirky and nothing like the pet shop.Is it just not achievable to have a gleaming fish tank with healthy fish?

Is it really only 13 litres or is that (I hope) a typo and it's 130 litres?

Yes goldfish are notoriously messy. Having a filter will help a lot - if you already have one it maybe its just not matured enough yet to have the required effect or it maybe too small for the tank.

A 13 Litre tank is no where near big enough for goldfish, you need a much larger tank with a good filter for it to be clean.

if you had a bigger tank, your water would be clearer.
i started with a small tank (11 litres) and it was a never ending battle to keep it clean and fresh, the water always looked filthy.

with goldfish you ideally want an oversized filter on a massive tank.
in my case i had an undergravel filter running alongside and internal fluval filter
this was a 60 litre tank and i had crystal clear water.

I had fancy goldfish, which still need a lot of space, but not quite so much as standard goldies
while it was clean and generally disease free, it was far from the ideal size.

my fish were stunted and lived to about 6 years old.
the tank has had mice in it since, but i doubt i'll ever have a goldfish tank again.

as fort he snails, they're not really that good at being algae cleaners, in fact, if they're ramshorns or generally small, you might find your fish will eat them

my Ollie fish was a serial snail murderer