There are a total of 8 Datacrons on Corellia, but each faction can get only 7 of them, 2 of the Datacrons here count towards Quesh's.
Datacron 1 - Republic and Empire
Codex Entry - Galactic History 81: The Battle of Telos Four
Coordinates: -2661, -3115
The Datacron is located within Labor Valley, the Advanced Product Research Sector. You need to go to the steel beam that's collapsed on the building at -2492, -3081. You need to go up the beam, then on the steel ledge, circle it to its right until you reach its end (the wall). Then, with the wall on your right, you need to move forward, jumping on the next steel ledge..keep walking forward on that ledge, then make a slight right (follow the ledge), keep forward until you reach the refinery-like building (with fire going out a pipe). You'll notice that near the right wall, there's a big pipe that leans down - you can jump on that. Go up the pipe until you reach its top, turn left and jump on the steel building (with beams) which connects to the pipe. After you've jumped, do a right, then left on the massive beam, walk forward until you see a steel road underneath you - jump on that road (in your right). Turn off Sprint and you'll notice a thing grey pipe that sticks out the road in its left - carefully walk BACKWARDS on that pipe just until you can safely fall down to the inferior level of that road (5 meters max). Fall down and you'll notice the Datacron at the end of the inferior road.
Datacron 2 - Republic and Empire
Codex Entry - Galactic History 82: Darth Traya's Return
Coordinates: -2754, -2007
This Datacron requires a bit of jumping around but it's easy. It's located within Labor Valley, Central Workforce Habitation. You must begin walking on a pipe at -2897, -2074 (near some piles of nicely stacked missiles). Once you reach the top of the pipe, you'll notice a canvas in its right, jump on that canvas. You now need to wait for a moving crane (with an Imperial Shuttle attached) that comes over the canvas - jump on that shuttle and ride it until the next platform (also full of nicely stacked missiles). Now run over to the other side of this platform and jump down onto the large crate (it's a fenced area) then jump to the ground. You'll soon notice a steal beam leaned towards a a big stack of crates. Go up this beam straight to the top of the pile. Now you need to go to the other side of the crate pile, which requires a bit of jumping since there are gaps between the crates and you will fall. At the end of the "crate platform", you'll notice a vertical-moving steel beam. Wait until it gets lower so you can jump on it. Wait until the moving beam reaches a high position, so you can jump on the crate on your right side (SW). Now keep moving to your South (jump onto that steel grid), you'll see a stack of missiles in the center, walk in its right, then you'll notice a steel beam leaning to a crate in your left, walk on top of it and there's the Datacron.
Datacron 3 - Republic and Empire
Blue Matrix Shard
Codex Entry - Galactic History 62: The Great Sith War Ends
Coordinates: -2423, -1062
The Datacron is located also within the Labor Valley - Derelict Service Area and it's probably the easiest Datacron on this planet. You just need to kill several droids and at the end of a hidden pathway, there's our Datacron. So, the beginning point is at -2305, -987, South-East of the map. When you reach those coordinates, you'll see a holographic door and you'll be able to enter a patchway (hallway if you like). Keep on walking until you see the Datacron on top of a crate. Jump on that crate and..it's yours.
Datacron 4 - Republic and Empire
Codex Entry - Galactic History 80: A Return from Exile
Coordinates: 3426, -3210
The Datacron is located within the Government District - Port Pevaria, under a catwalk in Port Pevaria. There's a bit of a hassle for Empire players since they need to tress-pass a Republic quest hub. The starting point is at 3258, -3105 and you need go to 3415, -3322 (northeast corner of the map - it's an area were mounts aren't allowed). After you reach that point, looking down, you'll notice a set of pipes that run on the side of the building. Jump down on the pipes and follow them until you see the Datacron at 3415, -3213 (to your left and below - it's on an invisible platform). At this point, you need to get close to the wall that blocks the pipe you've been following until now and jump down on the Datacron platform. To leave the area, you either need to type /stuck or commit suicide.
Datacron 5 - Republic and Empire
Codex Entry - Galactic History 78: The Sith Triumvirate
Coordinates: 3143, -1793
The Datacron is located within the Government District - Coronet Museums area. The starting point is at 3118, -1842. There's a weird looking, rusty steel beam leaned against a shattered column which has a glowing bomb on top of it. You need to climb the rusty beam, until you reach the column where you'll notice (on the left side when facing the column), a vertical moving thin column (very slow moving). You need to get on top of that to reach the top of the shattered column (where the bomb is). Once you're on top, you'll notice the Datacron on a ledge southeast (in front as you get down the moving column). This part is a bit tricky since you may not succeed from the first attempt. Now all you need to do is face the bomb, with the Datacron exactly at your back, click the bomb, which will throw you on the Datacron ledge. The trick is that you need to be positioned exactly on a straight line between the bomb and the Datacron - use your max zoom out function to approximate and measure better. It's not hard but if you position yourself 2 steps left or right, the bomb will throw you anywhere but that ledge.
Datacron 6 - Republic and Empire
Green Matrix Shard
Codex Entry - Galactic History 61: The Brotherhood is Broken
Coordinates: 700, -1890
For this Datacron, you'll need the MGGS (Magnetically Guided Grappling System)
(which can be bought from the vendor Lain-Ricie at 1869, 1091, in Alderaan - Juran Mountains). This item can be used to get several Datacrons including the +10 stats final one.
The Datacron is located in Axial Park - Archival Square, starting at 411, -1840. You need to enter the Museum of Starships and if you turn right, you'll see an elevator. You need to take this elevator to Rooftop Shuttle Pad and on the roof, you'll see an Imperial Shuttle. You need to climb the shuttle, and go up its right wing. (as you look at it the first time). From the wing, you need to jump down on the wall beneath it. You need to run east now on along this wall until you reach the coordinates 341, -1790. Looking down, you'll see a lower roof top, jump down on it. Make your way around the roof (left then right) until you reach the far corner of the roof. If you reached that corner, you'll see a big tree down on the ground. Facing the tree, it's upper right side, you'll notice there's a building past the tree and on it's rooftop, the Magnetic Stabilizer on which you can use the MGGS. Right click the Magnetic Stabilizer and you'll be pulled on that roof. Once on that roof and facing the Magnetic Stabilizer, go to your right (you'll notice a tunnel entrance - go through the tunnel) and follow the tunnel until you'll see a big crate with the Datacron on top of it.
Datacron 7 - Empire Only
Codex Entry - Galactic History 79: The Conclave at Katarr
Coordinates: -2404, 2949
This Datacron is located in Incorporation Islands and it's one of the hardest to get Datacrons in this game. You first need to go to the ladge at -2294, 2885 (where the character arrow is on the below map). If you look closely to your right, you'll notice the Datacron onto a beam. If you look down, you'll notice 2 platforms, one coming from the right (from the datacron) and one coming from the left. You need to jump first on the platform that comes from your right (as you look down). The trick is to jump on that platform before it interesects with the left platform. Timing and syncing your jump is the kye here, if you miss you'll instantly die. Once you jump on the right platform, wait for the left platform to pass it underneath and jump on that. Ride the platform until it reaches the Datacron and get it.
Datacron 8 - Republic Only
Codex Entry - Galactic History 79: The Conclave at Katarr
Coordinates: 702, 1716
This Datacron is located in the Blastfield Shipyards - Hyperdrive Installation Zone area. You begin at at 1125, 1662 and you need to follow the building ledge all the way around the building. You can use your speeder for this one. Once you reached the 3rd steel beam (around 1000, 1793), you need to jump on it and go straight up. Now turn around and jump to the cross beam across it. Now go to your your right, then right again..until the steel ledge ends. You'll notice in your left a brownish beam with some pipes..jump on it. (it's a bit tricky but it's easy). Once you jumped on it, go 2 steps forward, jump again (it has another layer of pipes), turn around, look up (you'll notice a steel platform)..jump on that also. So basically, you need to jump 3 times to reach the upper steel platform. (coordinates: 936, 1755). Once you get on top, you'll notice some Imperial black containers in your left. Jump on those containers, then jump on the large crate at their right. Then you need to jump onto the ship (jump on the left ship cannon first). Once at the top of the ship, look West and you'll notice a large crate underneath the ship's wing. Jump on that crate then at its northwest corner, you'll see a light brown steel beam. Jump on that beam, for forward until you reach the brown steel tower, go around its left and then you need to jump on the black pipes in front (as you did left at the tower, before you get around the right of the tower). Once over those pipes, you need to fall slightly to your right, on the building's ledge. Follow the lege until you get to the next building (the ledge and the next building are connected with some pipes, walk carefully on those pipes). Keep walking forward until the ledge ends and you need to fall down to he ledge in front (there's no need to jump). Follow that ledge until you get to its end. There, you'll see a steel beam leaned against another ledge to the right. Follow that beam, go right and you'll see the Datacron.