"There are no fish here."
Translation:Тут немає риби.
Is this how you would say it all the time? Or would немає риба тут also be accepted?
«Немає риба тут» is definitely wrong. «Ри́ба» is the nominative case form, and to express absence, you use the genitive case with «немає».
When speaking about word order, «нема́є ри́би тут» is not alltogether incorrect but it sounds less natural than «тут нема́є ри́би». Ukrainian tends to put the known piece of information in the beginning of the sentence, and the new information in the ends. So, «тут нема́є ри́би» tells us something new about this place, about «тут»: it less us that this place lacks fish.
«Нема́є ри́би тут» tells us something new about the absence of the fish: that fish is absent «тут», in this place. While it's a possible sentence, it's useful in less situations.
However, there's one caveat. You can mark the new information by emphasising it with intonation. So, «Нема́є ри́би тут» with «нема́є ри́би» emphasised by intonation is roughly equivalent to «Тут нема́є ри́би». However, this is not the default word order, you use it if the absence of fish is really important. We usually avoid this word order, and use the neutral word order.