The Pillar Push mission puzzle takes place in Theed Palace over in Theed. It involves having to push various pillars and flip switches
Head inside the Theed Palace and speak with the Theed Palace Guard, who will mention that he has just finished polishing the floor, and more importantly, that these pillars can be moved.
Now above these pillars is a total of four levers that need to be activated, once one has been activated there will be a 30 second countdown timer. We will have to activate all of the levers before the timer runs out if we want to achieve this one.
In order to make thins more easier and simpler I would suggest either using Jango Fett or any other character with the ability to glide around freely. This way we can move around faster and reach those other levers with fewer difficulties.
Position the pillars so that you can reach the levers above and then climb up one to begin the countdown timer.