Call of Duty: Black Ops II

Story related achievement. Can't be missed

This achievement will unlock after completing the fourth mission "Time and Fate", no matter what difficulty you are playing on.

"Man of the People" achievement is also obtainable at the beginning of this mission.

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I'm not taking credit for the other solution, that's why I'm only putting a link and not the complete solution.

Mission 4 - Time and Fate

In this mission, you will be playing as Menedez and as Mason. This mission will give your more insight as to why Menedez is doing what he is doing in the future.

Mission Challenges:

1) Eliminate 7 PDF soldiers with a shotgun in under 10 seconds - PDF soldiers are the first ones you encounter in the mission. They are the ones ravaging the village. You start out with a shotgun in your possession. The best time to complete this is while you are in the frenzy mode. You also want to be going for Man of the People achievement during this time as well.
2) Eliminate 10 PDF soldiers with a truck mounted MG - After you leave the barn and are just outside the house where Josefina is, a truck will drive into the courtyard that has a MG mounted on it. Use the MG to eliminate 10 soldiers in the courtyard.
3) Rendezvous with Josefina in under 140 seconds - This starts as soon as you gain control of Menendez. Your main objective at the start of the mission is to reach Josefina. You have 2 minutes and 20 seconds to reach her for this challenge. You will be a little pressed for time to complete the 3 above challenges and do to this one all in one go. You may have to sacrifice one challenge for the other.
4) Eliminate 12 Cartel soldiers with Molotov - After you reach Josefina and go through the cut scene, the cartel will now come into play. The Molotov are located in the first area you come to and require the access kit to get into the crate. Make sure to make good use of the Molotov as there are no resupply points for them. One very good spot to use a few of them are when you reach the MG in the little shack. Take the stairs up to the right and in the hut on top of the hill, there are normally 4-8 soldiers in there.
5) Crash an enemy truck - This is done just past the hut where they moltovs were used. A truck will come at you and you will need to kill the driver and make him crash into the fence.
6) Eliminate 10 Cartel soldiers with mortars - These are located in a locked garage when you make it to where Woods spots Noriega from a balcony. Make good use of the mortars as there are no resupply points for them.
7) Eliminate 10 Cartel soldiers with a machete - This is located in a locked room when you make it into the Cartel's drug operation center underground.
8) Locate the evidence of a CIA presence - It is located in the room where the cartel are attempting to burn the evidence. When you are looking at the furnace upon entering the room, take a right and it is sitting on the desk
9) Collect all three intel - The first intel is located on a wagon at the right end of the barn where the horse run at you. The second intel is located in the right watch tower in after you pick up the mortars. The third one is located in the Cartel's drug operation center underground in one of the side rooms before reaching the area where the Cartel are burning the files.
10) 100% survivability - Complete the mission without dying or failing a check point.

'Man of the People' is earned while you are playing as Raul Menendez when he is in his frenzy mode at the beginning of the mission. You will need to save 4 people who are been brutalized by the PDF. The video below will have the location of all 7 people to save.(Video Time: 00:52-02:08)

This achievement is for the fourth mission, Time and Fate.

Just as a warning, there's a level breaking bug on this particular mission. After you take control of Mason and progress to the stage where you see Menendez running into a barn, you will come to a large courtyard. Before this there is a garage to the right where you pick up some mortars and you can also refill your ammo.

After this point you will see an open area and steps leading up to the courtyard. The important thing here is to not enter via the front arch but to enter via the bell tower to the right of the entrance instead. You have to go to the top and provide cover. When all the enemies are cleared out, you will be told and your team will move to the centre of the courtyard.

If you enter through the arch two bugs can happen:
1) Your team may not go the centre of the courtyard and will just look like they're taking cover.
2) The mission may pass this point but you will not be allowed to go down a ladder to continue.

The only way around these bugs is to restart the mission.