In my modest opinion the best way to hunt a capybara is to stalk it through the thick river bush, after a rain is also good because everything is wet and you don't make much noise, also in winter they take sunbaths at midmorning to warm up after a cold night.

You also can hunt them when the river is flooded so they go out of the bush, or at night with spotlights, from a canoe also is nice, etc. The first one it's the more challenging, but obviously the success rate is much lower. But I think it depends on the area you hunt, a swamp will be impossible to hunt it on foot.

The meat is good and if you don't want to waist too much, a 22 rifle is enough if you aim to the head.

You also can make a whistle (very easy) that imitates the male, they will come "to take a look" at the intruder.

Any way you hunt it you will enjoy it, that's sure.
LG