My Danish friend says there shouldn't be a "t" at the end of "fuldstændigt", since the subject "fisken" is "en fisk" not "et fisk".
I think the "t" is there because "fuldstændig" is used as an adverb, so it goes with "red" rather than with "the fish". So if you say "the fish is complete" it would be "fisken er fuldstændig", but now you say it's completely red, so "fuldstændigt rød". (Not a native, just trying to make sense of it.)
It's the red that is complete, not the fish. Adverbs don't decline with the subject, because it's not the subject that they're affecting. See the lesson notes.
(en) fisk = (a) fish [singular indefinite]
fisken = the fish [singular definite]
(flere) fisk = (several) fish [plural indefinite]
(alle) fiskene = (all) the fish [plural definite]