Coordinates: X 552 , Y 549
This is probably one of the easiest Datacrons to get in the entire game. For Republic players it is located in a friendly area, meaning there is absolutely no danger in retrieving this Datacron. For Imperials you will need to dodge a few elite Republic guards and possibly deal with a Republic player or two but nothing you can't handle. Now that you're probably itching to know, this Datacron is located atop the Republic base of Ilum. It's safely tucked away inside a hut atop the base around the coordinates (552 , 549).
Coordinates: X 920, Y 1072
This Datacron is located in far southeastern Ilum, to reach it you will need to run through a snow storm and an exhaustion zone. To get here safely follow the southern wall around to where I am on the map in (Screenshot 1). The exhaustion zone will only bring you to about 50% health before you make it back to safety and can retrieve the Datacron. Be careful getting down here if you're Republic as there are many Imperial elites just north of where this Datacron is located.
Coordinates: X 106, Y -75
This Datacron is located in a canyon in the center of Ilum (Screenshot 1 & 2) and much like the other Datacrons on Ilum, is extremely easy to get. There are two ways to get to this Datacron, the first way is to jump down into the canyon (don't just jump straight down, jump from ice ledge to ice ledge so you don't die) and the second way is to take an elevator down. I prefer just falling down into the canyon and then either using Quick Travel or taking the elevator back up.
Take into note that if you're Republic you will want to take the eastern elevator up and if you're Empire you'll want to take the western elevator. If not you'll be fighting some mobs when you come up.
Coordinates: X 311, Y -375
This Datacron is located in the Imperial Base Camp of northern Ilum. Much like the Yellow Matrix Shard piece is, this Datacron is protected by a member of the Imperial faction (the Yellow Matrix Shard it was protected by a Republic mob, but you get my point...) Despite being in the middle of an Imperial base this Datacron is still rather easy to get if you're Republic, even without Stealth. (Screenshot 1) has a look at the Datacron from a distance, the frozen lake nearby the base.
If you look close enough you can see the Datacron inside the hut directly in front of me. From where I am now it's pretty much a straight run in to get the Datacron if you want to avoid all of the Imperial forces. To see the exact location of the Datacron on the map and in game take a look at (Screenshots 2 & 3)
Coordinates: X 300 , Y -1565
This Datacron is located in far northwestern Ilum but to get to it you will need to go down an icey slope in northeastern Ilum (Screenshot 1 has it marked). Where the big white X is on the map is where you will find the slope. You can actually kind of see the slope on the map if you look close enough. Once you're down into the icy chasm you'll want to run all the northwest to where I am on the map in (Screenshot 2). Here you will find an entrance to a cave with a lot more of those Lisk mobs as well as a big champion mob called The Crystal Eater.
All the way in the back northern end of the cave you'll find the Datacron. If you're looking at the Crystal Eater it's to the left, or, in otherwords, straight ahead from where you enter the cave.