Van Leuwenhoek observed the first protist in 1674, but his description of it was somewhat superficial and fragmentary:
Passing lately over the Sea at a time, when it blew a fresh gale of wind, and observing the water as above described, I took up some of it in a Glass-vessel, which having view'd the next day, I found moving in it several Earthy particles, and some green streaks, spirally ranged, after the manner of the copper or Tin-worms, used by distillers to cool their distilled waters; and the whole compass of each of these streaks was about the thickness of a man's-hair on his head: Other particles had but the beginning of the said streak; all consisting of small green globuls interspersed; among all which there crawled abundance of little animals, some of which were roundish; those that were somewhat bigger than others were of an oval figure: On these latter I saw two legs near the head, and two little fins on the other end of the body: Others were somewhat larger than an oval, and there were very flow in their motion, and few in number. These animalcula had divers colours, some being whitish, others pellucid: others had green and very shining little scales; others again were green in the middle, and before and behind white, others grayish. And the motion of most of them in the water was so swift, and so various, upwards, downwards, and round about, that I confess I could not but wonder at it. I judge, that some of these little creatures were above a thousand times smaller than the smallest ones, which I have hitherto seen in chees, wheaten flower, mould, and the like.
van Leuwenhoek, A. 1674. More observations from Mr Leewenhook in a letter of Sept. 7, 1674 sent to the publisher. Philosophical transactions of the Royal Society of London, 9: 178-182.
Did he later redescribed them more thoroughly?
If not, when and by whom was an eukaryotic cell properly described for the first time?
What strikes me the most in this first description is that he doesn't seem to acknowledge what's inside the cell (apart from "others again were green in the middle, and before and behind white, others grayish"), despite the fact that some organelles (nucleus, chloroplasts, etc.) should be visible with an optical microscope.