The easiest way to accomplish this is to have the warrior in a large centrifuge that speeds up to simulate enhanced gravity on the axis perpendicular to the spin - think of the gravitron ride - you can turn sideways on the walls at a sufficient speed.
Since your survivable g-force is limited by physiology, your rotational speed could only reach a tiny fraction of c before any living organism would be crushed into jelly striated by chemical weight.
As mentioned in the comments, there would be no appreciable time dilation when training at any survivable g force. It might be measurable in picoseconds, but nothing the average person would notice.
Addendum:
From the wiki article on gravitational time dilation:
On the other hand, when g is nearly constant and gh is much smaller than c^2, the linear "weak field" approximation T_d = 1 + gh/c^2 may also be used.
Conversely, we may approximate the effects of increased gravity as reducing the distance between the warrior and the planet (eg: everyone outside the room is at a "farther above the gravitic center of mass on the planet.")
Since gravity increases/decreases by the square/root of the distance, so a person twice as close would experience 2^2 as much gravity. Extrapolating for the desired gravity multiplier x = h^2), we have:
$$T_d = 1+\frac{g*\sqrt{x}}{c^2}$$
Assuming an earth-like original gravity, moving to a 9G environment (considered the maximum survivable vertical G by modern airforce pilots), then x=9, root x=3, and the equation neatly wraps up as:
$$T_d = 1+\frac{3g}{c^2}$$
$$T_d = 1+\frac{3(9.80665 m/sec^2)}{(299,762,458 m/sec)^2} = 1+3.274e^{-16}$$
For scale:
$$3.156e^{-16} nanoseconds = 1 year$$
Basically, the outside world would gain ten nanoseconds a year compared to the area inside the room.
Further addendum:
If we assume that native gravity for the aliens is 1 billion times earth gravity (because they live on the surface of a neutron star?) and we're talking about a 9-fold increase in native gravity (don't forget, whatever natural physiology that the aliens have is adapted to their evolved environment), then you're still only looking at:
$$T_d = 1+\frac{3g}{c^2} = 1+\frac{3(9.80665*1,000,000,000 m/sec^2)}{(299,762,458 m/sec)^2} = 1+3.274e^{-7}$$
$$3.15569e^7 seconds = 1 year$$
Which still is only a 10 second gain per earth-year for the outside world. It's going to be noticeable at that point, but you only really experience significant time dilation at points where g*h approaches C, and at that point you need to use a different equation and most large solid chunks will rip themselves apart.