No large amount of time dilation is likely to be practical, even with laser propelled light sails or antimatter. And the heat load on the vehicle from running into interstellar matter would be very high.
The more massive DM particle issue I discussed might be problematic even with very little time dilation.
Whatever tech is used, it'll need to be something really fancy (as in new, fancy laws of physics being bent in fancy ways) to make near light-speed travel feasible.
Even Alcubierre-White warp drives would create interesting problems because compressing spacetime in front of the ship would heat up whatever matter is there.
Unless something miraculous happens, I don't think we'll live to see these problems in real life, but, if we do, it'll be fun to work in solving them.
The more massive DM particle issue I discussed might be problematic even with very little time dilation.