Accelerating consistently at 1G (and then -1G for the second half), should take 6 years of proper time (from the perspective of the traveller) to get there.
Yea, actually the problem is not at all that we’d need too much acceleration for the human body. Accelerating at 1g for a couple years gets you to preposterous speeds (and we don’t even need any artificial gravity nonsense!). The problem is that accelerating at 1g for years would require a ridiculous amount of energy.
In his 1958 juvenile novel Have Spacesuit, Will Travel (I read it years later as a tween), Robert A. Heinlein described this as a "skew-flip maneuver" that would get someone from Earth to Pluto in five days at 8G (!). And apparently E.E. "Doc" Smith described it even earlier.
