Dulfy has guides for the Imperial and Republic versions of these achievements:Hey folks,
We wanted to pass on a heads up about some Achievements which will be coming out of the game with Game Update 4.0.
Category: Citizens of Makeb
Mass Exodus
Hero of the Citizens of Makeb
Making the Connection
Category: Makeb Imperial Forces
Contain and Control
Hero of the Makeb Imperial Forces
Well Connected
All players who complete Making the Connection and/or Well Connected achievements before they are removed will be receiving a Makeb Gazebo decoration in the mail around the time Game Update 4.0 launches. If you don’t have those achievements but you are looking to get them before they are retired, now is the time! We’ll see you all on Makeb.
Republic: http://dulfy.net/2013/05/12/swtor-makin ... ent-guide/
Sith: http://dulfy.net/2013/05/11/swtor-well- ... ent-guide/
These achievements are related to the Staged Weekly quest chain that is unlocked when you've completed the main Makeb story. So if you skipped Makeb you'll need to run through the story to access the weekly.
You will complete the first two achievements while working on the third whether you are Republic or Sith. The trick to the third achievement (Making the Connection/Well Connected) is that you must complete certain quests in a specific order to complete steps of the achievement and that cannot be accomplished by one character in one week. That means you'll need to work on a different step of the achievement in a following week or complete the steps on different characters (of the same faction). Since achievements are legacy based you spread out the questing on multiple characters who have access to the weekly.
As for the decoration, Bioware hasn't officially shown what it is, but my guess is that the Makeb Gazebo is this:
A few of the quests are Heroic-4s which can still be tricky even at level 60, so if you need hand with anything, please don't hestitate to ask for help!