For this achievement, instead of driving around all speedy gonzales like the game intends you to do, when I got my hostage I stayed barely above the 'too slow' limit, and drove in circles.
Head on over to the Saints Row Loft Crib and go a bit north to the bridge. Grab any car and park it over both the incoming lanes of traffic so cars pile up there. Scan through them to find one with an extra passenger and hijack it. Start the hostage and drive back to your crib. When you get to the circle right beside your crib, simply drive very slow (not slow enough for the hostage to jump out) and keep going around the circle. If you go slow the cops cannot screw you over very bad (i.e. terrible crash while going 9999mph). It is hard for them to knock you off course and there usually only ends up being 1 or 2 cops following you in the circle. After the negotiation is complete, head over to the bridge again and repeat. a fair while later, this achievement will unlock.