Fallout: New Vegas

I have written 2 solutions 1 with and 1 without spoilers.

1st no spoilers

Load up the save you made after the last achievement popped. Speak to Daniel and tell him you agree with him and will help get everyone out. Complete the quests then given to you. There are markers on your map and your pip has the information you should need.

Now you have done that reload your save and do O Daughter of Babylon - Crush the White Legs if you need to. If not then that should wrap up all the Honest hearts dlc achievements

2nd *SPOILERS*

Load up your save. Speak to Daniel and tell him that you agree that getting everyone out is the best plan. Once the conversation is over you will have a loading screen. Once its loaded you will be next to Joshua and he will explain what is happening. Tell him alright lets go. You will now have 4 quests in your pip boy.
1 main quest:
*Flight from Zion
and 3 optional quests:
*Retake the bridge
*Sanctity of the dead
*Prisoners of war

I will now cover the 3 optional quests these are not needed for the achievement but are still fun. If you don't want to skip ahead.

First Prisoners of war. Select this as your active quest, This will give you 5 markers to follow. Head towards them since you cannot fast travel. You will have to go south and loop back up past the Zion ranger station to get to them. Once you get to the markers you will discover Ranger substation osprey and there will be a fair few white legs to fight. Once they are all dead pick the lock on the station and free the sorrows tribal people. Thats the quest done.

Second retake the bridge. Select this as you active quest. This will give you a marker leading to East fork bridge. Start walking there since you still cannot fast travel. Once you get to the bridge you will see the 3 markers on the map represent 3 white legs that you need to kill. So go kill them. Quest complete.

Third sanctity of the dead. Select this as your active quest. This will give you quite a few markers on the map. Head to the marker by its self, its the most north marker of them all and yes more walking since fast travel is still not aloud. Once you reach the marker you should find 2 sorrows tribal people. Speak to them and tell them you will go kill the white legs and that they should go.

Now head to the other markers that are all grouped together these are the white legs you need to kill. There are 5 all together. They are very to close to where you are. Once they are all dead thats the quest complete.

****If you are skipping the optional quests this is where we start the main quest so,

Now on to the main quest - Flight from Zion. Select this as your active quest if you need to, This will place a marker leading you to Pine creek tunnel. So get walking. Once you get near to the tunnel there will be some white legs and sorrow tribal. Only kill the white legs. Once they are taken care of the objective will be complete and a new one will be given - deal with salt upon wounds. Keep following the marker on the map.

Once you reach the tunnel Salt-upon-wounds will speak to you. If you have a speech skill of 75 or more you can talk him into to leaving, if not you fight and kill him. You will now have to go and speak to Daniel who is just turning up. Tell him you have done everything you can for them. They will all leave and you will regain control of you character stood in front of the tunnel with a detonator in your hand. Blow the charge and your achievement will pop.

Now you have done that reload your save and do O Daughter of Babylon - Crush the White Legs if you need to. If not then that should wrap up all the Honest hearts dlc achievements

Story related: Make sure you save right before talking to Daniel when you complete his quests involving getting rid of the white leg traps, the yao guai, and the camps (In a foreign land achievement will pop at this point). This way you can get both O Daughter of Babylon and May my hand Forget its skill achievements.