"The sea is both blue and green."
Translation:Deniz hem mavi hem de yeşil.
"...-in ikisi(ni) de" is for "both" in the sense of "the two (noun)s".
Here, you're not talking about "both seas" -- your sentence would be "Both of the seas are blue and green", except that it's wrong because you used the accusative (ikisini) for the subject of the sentence.
Instead, you're talking about one sea that is "both ... and ...", and you need the "hem ... hem (de) ..." construction for that: "Deniz hem mavi hem de yeşil".
Compare also: "Both the sea and the island are blue": "Hem deniz hem (de) ada mavi(dir)".
Here again, it's not "both seas" or "both islands" as in two of the same object, but you want to say that not just one thing but also the other thing is what you are talking about, so "hem ... hem de ..." is appropriate.