Star Trek Legacy

As digitalwar4 stated, use only the Enterprise. This will unlock the Lone Wolf of Makus achievement as well! Double pointage! Also this is easiest done on easy. One way to help you a little is to not warp straight over right when the mission starts...instead fly vertically straight up for a little while, then warp over to the Bird of Prey. Come down on the Bird as far as you need to get your target lock and/or tractor beam. All the ships patrol on a horizontal plane basically. You can avoid a lot of enemies this way. Once you get the tractor beam, fly up vertically, then over to your base. I also found it easier if you put your power half way between shields and engines. This way you still have little pep in your step and some extra shielding.

To obtain this achievement you cannot destroy any enemy ships. Warp the Enterprise and only the Enterprise to the area where the Bird of Prey is located (all the way at the bottom of the map). Kirk should say "there is the ship" etc etc etc, target that ship and go crazy with weapons. Remember to only target this ship. Once its disabled warp away. Chances are your shields are a little low. Let your shields recharge and if you need to repair your ship.

Once finished recharging / repairing warp back to the location of the Bird of Prey, it will remain disabled. Lock a tractor beam on the ship and set your course for your star base at the top of the map. There will be tons of Klingon's chasing you so its best to put all your power into shields right away. If they focus their fire on the Bird of Prey you can push more power towards engines so you can attempt to out run the Klingons. If your shields are coming close to failing then let the tractor beam go and warp away.

Take the ship to your base and if you haven't destroyed any enemy ships then you should get this really nifty pop up saying achievement unlocked.

To get this easily on any difficulty and the no starbase achievement.

Essentially you can bait the target ship to follow you the end goal under his own power.

From enterprises view warp to the top left of the nebula, get close enough to the shipyard to start the cutscene. Confirm the target ship is following by looking for his red square and see that he's closing the distance.

Now that he's following you warp to the centre of the starbases. Wait for it to come close i'd say within 3000mm then warp most of the way back to close to where you started. have all 4 of your ships open fire on the targeted ship and tow him the 500mm to the end goal ending the mission almost instantly. I did this on admiral difficulty quite comfortably in about 6-7mins.