The poet represents the daffodils as a group of dancers who (perform) a beautiful dance.
Is it correct to write (perform) or I should write (performs).
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To me, "a group of dancers who perform..." sounds most natural. This is equivalent for me to ""a group of dancers that perform...".
It would also sound OK, although perhaps not as good, to say "a group of dancers that performs...", treating "group of dancers" as a collective noun that takes the inanimate relative pronoun "that" and singular agreement.
I am certain I don't like the sound of "a group of dancers who performs".
There are a few tricky parts to this example, so even though there are many previous questions on this site about subject-verb agreement in relative clauses, I'm posting a provisional answer here, not just a comment, to try to summarize all of the relevant information. (I can't find any single pre-existing post that seems to fully answer your question.)
A phrase like "a group of dancers" actually is a noun phrase containing another noun phrase. The embedded noun phrase, "dancers", is definitely plural. The word "group", the head of the larger noun phrase, is a "collective noun", which can be treated as singular or plural depending on various factors (described to some extent in the answer to Is "group" singular or plural?).
A relative clause can attach to either the embedded noun phrase, or the larger noun phrase. This is called "attachment ambiguity", as described in a comment by John Lawler on the question "A group of people that (ARE) or A group of people that (IS) - proper usage?".
However, the choice of relative word is determined to some extent by the animacy of the antecedent. The relative word "that" can be used for animate or inanimate antecedents, but the relative pronoun "who" is restricted to animate antecedents.
When a collective noun is treated as a singular entity, it often sounds awkward or outright incorrect to use the animate relative pronoun "who". This I think is the reason for Edwin Ashworth's comment
You certainly can't use '... dancers who performs ...'
You can see a more detailed description of the factors influencing "who" vs. "that" (vs. "which") as the relative word for a collective noun in the answers to "What is the correct relative pronoun for “government”?" and other questions linked to that one.
Because of this, if the animate relative pronoun "who" is used in this sentence, many people will assume the relative clause is attached to the embedded noun phrase "dancers"—which is plural, requiring the third-person plural inflection of the verb "perform".
The attachment of the relative clause would be more ambiguous if the relative word "that" were used.
The relative pronoun "which" is generally only used with inanimate antecedents. If the relative pronoun "which" were used in your sentence, people would likely expect singular verb agreement in the relative clause ("a group of dancers which performs..."). However, this still sounds a bit strange to me.
Even if we consider the relative clause to be attached to the overall noun phrase "group of dancers", rather than the embedded noun phrase "dancers", there are some semantic reasons for preferring to treat "group" as plural rather than singular in this context.
As described in the linked posts about collective nouns, they tend to be treated as grammatically singular when they refer to something that is conceptualized as a single unit or something that is acting all together. The dancers are working together to perform "a dance" (which could be thought of as a single, unitary action) in this context, but on the other hand, the noun phrase "a group of dancers" is used in this context after the plural noun phrase "daffodils".
My intuition is that in this sentence, the plurality of "daffodils" would tend to have the strongest effect on the treatment of "group (of dancers)", and would cause people to favor plural agreement. But that's just a guess.