Explain the differences in challenges faced by a phytoplankton compared to a fish. Specifically, discuss how their Reynolds number affects their...

Since they are so much more massive, metazoa such as fish have much high Reynolds numbers than microorganisms such as phytoplankton. As a result, fish swim in turbulent flow while phytoplankton swim in laminar flow. The kinds of bodily appendages that are necessary for movement in turbulent versus laminar flow are quite different, and in general it's much harder to control your direction of motion in laminar flow. As a result, phytoplankton had to evolve to acquire nutrients from whatever they happen to flow toward, while fish evolved to seek out and consume the most efficient sources of nutrients (typically other fish).

Almost all organisms face the external challenge of predation (the only exception being apex predators such as sharks, orcas, and humans---and even then sometimes apex predators will attack one another). Phytoplankton have essentially no defense against being eaten, while the primary defense fish have evolved is simply to swim away as fast as possible---though by forming schools, fish can also reduce their individual probability of being eaten in a similar fashion to herds of land animals.

Another external challenge is competition with other organisms for the same ecological niche. Phytoplankton mainly compete with other phytoplankton---e.g. diatoms compete with algae---for sunlight and CO2. Fish compete with a variety of other organisms, ranging from other fish to cetaceans to jellies to molluscs. The ocean is a very crowded place.

As far as internal challenges, one is pressure. By being on a larger scale, fish face the challenge of pressure; pressure is largely meaningless at the scale of phytoplankton, but at the scale of metazoa it is extremely hazardous. Deep-water fish especially have had to evolve various mechanisms for resisting high pressure.

Another is respiration. Water cannot itself be respired by either plants or animals, so both must evolve means of extracting what they do breathe from water (namely, O2 and CO2), and in turn must live in water that contains sufficient amounts of dissolved gases.