There is only one noun phrase in the picture. That is, your answer would be "dark purple irises". "Slowly but surely" is not a noun phrase, but an adverbial phrase and "with the purple petals" is a prepositional phrase.
In this way, the complete sentence would be as follows: The flowers, dark purple irises, bloom every year in April. This NP is an apposition as the two nouns refer to the same thing (flowers/irises) and are placed immediatly after the other with no conjunction between them.