En efecto = Effectively,
empresa barroca = company undertaking barroque style works

En efecto, debemos subrayar la forma de colonización espiritual llevada a cabo por la empresa barroca, que tomaba a su servicio a los artistas ...

In fact, we must emphasize the spiritual colonization way undertaken by the baroque company, which hired the artists...

Espero haber ayudado! :)

We must really point out the way in which the barroquial enterprise carried out the spiritual colonization,...

"We are compelled to emphasize the spiriual "colonization" achieved by the baroque enterprise, which hired the artists..." -- I put "colonization" in quotes because the text is referring to a metaphorical, rather than a physical, act. Because there were no companies (in the modern sense) during the Baroque period, I used "enterprise" instead. The sense of the passage seems to be that the artists' hearts and souls were affected through the creation, at their clients' behest, of artistic works having some spiritual or religious content...

En efecto, debemos subrayar la forma de colonización espiritual llevada a cabo por la empresa barroca, que tomaba a su servicio a los artistas ...

We must indeed underscore the spiritual colonization carried out by the baroque enterprise, which took the artists into service . . .

My supposition is that we are not discussing a company that existed during the baroque period at all. Rather, a company with an extreme bureaucracy - calling to the writers mind the baroque style with its lavish ornamentation. I have used enterprise for the translation because it fits better with that image than company would to the American English ear. Likewise the phrase took the artists into its service is an appropriately antiquated one to carry the metaphor, rather than using the simpler, more modern hired the artists.
Hope this helps!