We work on research and development every day in order to keep tackling new challenges and meet new needs.
Literal
New things [dative-に] challenge-continue [for-ために], new needs [dative-に] respond [for-ために], daily R&D [dative-に] are-striving-[polite-ています].
Corporate marketing prose with parallel ~ために clauses. ~ために ('for the purpose of, in order to') is one of the standard purpose-marking constructions. The doubled structure ('for X, and for Y') is a stylistic flourish typical of company mission statements. ニーズに応える 'meet needs' uses the verb 応える ('to respond to, to answer'), which takes に for its object. 努める ('to strive, to make effort') with に marks what the effort is directed toward.