As it says, keep an Enterprise-era ship all the way through to the start of the Next Generation missions, which is a lot easier than it sounds. If you read my breakdown of the Mission-Specific Achievements, you'll note all the Original Series missions are accomplished with three vessels. That's because the fourth slot is an Enterprise-era ship that should be kept out of the fighting at all costs.
The easiest way to do this is to warp the ship to an unoccupied area of the map (the corners do nicely). The only missions you need to watch out for are "At the Gates" and "Omega". In "At the Gates", there's deadly plasma all over the place, so keep your Enterprise-era ship right where it is instead of warping it somewhere. In Omega, once you've disabled the dampeners, ALL of your ships will join up to attack the Omega Sphere. Before you do anything else, you
need to quickly warp your Enterprise-era ship out of the fight.
Once you've reached "Revelations", you'll get this achievement after watching the cut-scenes. You don't need to beat Revelations, so once you get the achievement, you can restart and sell your Enterprise-era ship (as it won't be
too effective in "Revelations"). Just make sure you actually got the achievement before you sell.