No, there is no evidence that Achilles was a real person.

The story of the Trojan War, and especially the Homeric epics, loomed large in the mind of the ancient Greeks of the historical era (i.e. after ca. 700 BC). But there is little merit to the idea that these stories were based on historical events (what, indeed, is a "kernel of truth"?); the epics, for example, are definitely not sources for the Bronze Age. For more on the use of the past in the imagination of the ancient Greeks, see my answer here (with further references).

Troy was located in the Troad, a region in northwest Anatolia; there really was never much discussion about this -- debates mostly focused in the modern era on whether or not Troy ever existed (the ancient Greeks and Romans never had this doubt), and once people like Schliemann took to digging around in the area, the question became more focused on where within this area the city had been located precisely. The ancient Greeks believed that some of the burial mounds in this region must have belonged to Achilles and/or Patroclus (in the Iliad, it is said that they would be buried together, with their ashes/bones mixed inside a single vessel). We don't know how they determined which mound belonged to what hero: no doubt someone just picked a mound and tradition developed around it (or not, as the case may have been).

When Alexander crossed into Anatolia to embark on his conquest of the Persian Empire, he supposedly visited Achilles's tomb, while his compatriot Hephaestion went to the one that they believed belonged to Patroclus (Arrian 1.11-12). How did they know which was which? We have no clue, but either the local people had just appropriated these tumuli for their own purposes -- tourism isn't just a modern invention! -- or Alexander simply picked a mound that was suitably heroic for his purposes. It didn't matter too much: the act of visiting a place where Achilles could conceivably have been buried was enough.

In the modern era, the first tentative excavations were conducted in the eighteenth century. Heinrich Schliemann also took a stab at some of the tumuli in the Troad, but the results were mostly disappointing: a lot of the tombs dated from the Archaic, Classical, and even Hellenistic periods, rather than the prehistoric era. (Of course, this supposes that the story of Achilles is somehow historical, which it isn't. So searching for his tomb is a fool's errand. By way of comparison: there is a bronze statue of Star Trek's Captain Kirk in Iowa -- that doesn't mean that James T. Kirk is anything more or less than a fictional character!)

A really good overview of the problems involved in locating Achilles' presumed tomb can be found in Jonathan S. Burgess's article "Tumuli of Achilles", published in issue 3 of Classics@ (2020). The website seems to have removed the page, but you can access the cached version of the relevant page here. An HTML version of this article is still available here.