In the popular merfolk topic, I always use the model of marine mammals, not water-breathing fish-like animals. They breathe air, that turbo-charged 20% oxygen fluid that enables the scale of metabolism that we enjoy as warm-blooded animals.
Recently, Dr. Mason debunked the Triton Gill crowd-funding scam (note: I was a major sponsor of the debunking video). Only, he did such a good job of showing how such a thing could not possibly work on a fundamental level that it also destroys any hard-SF portrayal of such a device (or gill implant).
In particular, a liter of air contains 200 ml of oxygen, and a liter of water contains (if you could remove it all perfectly) 5 to 10 ml of oxygen.
One of the earliest SF stories I dabbled with featured a gill-pack with the appropriate size and weight of a SCUBA system, but was a gill: it seems plausible that near-future technology could have a membrane that allowed disolved oxygen to be extracted, and that membrane would be folded and branched to have a high surface area, coming in contact with all the water that passes through, and long enough to process all the water before it passes out the other side.
The catch is that you would have to pump about 100 liters of water per minute through the device. In a device, that would be an enormous jet!
For a human-sized/human-metabolism animal, how could you process this much water over your gills? Note that adding to their expanse, such as a long train, would be more tissue to feed, too.
On the other hand, fish like tuna and baracuda exist, that are fast and have red muscles. I suppose they must use their high energy level in bursts only and take a long time to recharge. Exploring that idea is one avenue: but note that the brain takes a lot of power all the time (but see this question. But also, cold water has more oxygen.)
In short, how can be have a water-breathing animal that's not sluggish/torpid and has a large brain?