That would be Tá an turta beo. In this sentence you're classifying 'it' (é) as 'a living turtle' (turtar beo), therefore you use the copula.
It is confusing to teach beo as a new adjective when it seems to be proposed first here as a noun with the copula (same case with fíor), even if a correct English translation turns out to be the same in both cases with the copula or bí (or maybe I am missing something again, which is entirely possible - I'll check back notes).
edit: ok found my mistake, beo is used after turtle (and thus an adjective), and not after the copula or the é (which would make it a noun).
Beo isn't proposed an a noun anywhere on Duolingo, as far as I can tell, it's only ever used as an adjective.
Is turtar é - "it's a turtle".
Is turtar beo é - "it's a live/living turtle" - "live/living" is an adjective. Tá sé beo - "it's alive".
I realized my mistake after a few minutes. In the dictionary it came up as a noun in the listing first, causing a momentary confusion.
I guess to use beo as a noun, I could say something like:
Is beo é an turtar ("the turtle is a living being") ?
This is one of those cases where the dictionary entry might be a bit overly specific. It gives two very idiomatic examples, na mbeo agus na marbh and beo ná ceo, but I'm not sure that beo would normally be used to mean "a living being" as in your sentence (where "living" is still an adjective).
I'm not saying that Is beo é an turtar is definitely wrong, just that I'm not sure that the entry in focloir.ie really justifies it's use that way, and I'd look for some other sources before using it that way.
Shouldn't beo be lenited? I can't hear it in this audio. It sounds different from the audio of "Tá sé beo".
Why not "Turtle is alive."...?
I'd be very likely to abbreviate that in speech to "Turtle's alive." Like I would "Bull's angry." "Dog's barking." "Cat's sleeping." etc but the structure is the same.
"alive" is an adjective. In "The turtle is alive" you have a verb, a noun and an adjective - tá an turtar beo.
In "it is a live/living turtle", you have a pronoun ("it") and a noun ("turtle"), so you use the copula rather than tá - Is turtar beo é.
The adjective beo is not really relevant to that grammatical decision - you can just leave the adjective out and get "It is a turtle" is Is turtar é.