Get an MGGS
The MGGS item allows you to use hidden grapple points around the galaxy. You may have already gotten this item if you went after previous grapple hook datacrons. The MGGS item can be bought from a vendor named Lain-Ricie hidden in the Juran Mountains of Alderaan. The MGGS item can be placed into your legacy bank and swapped between characters, but as far as I can tell it can’t be bought on the GTN or traded to a friend.
The closest Republic quick travel point is the House Alde quick travel point and the closest taxi is the House Alde Library Thranta speeder point, on the right side of the map, and then run quite a ways south along the mountain paths to the vendor.
The closest Imperial quick travel point is the Outpost Talarn quick travel point and the closest taxi is the Outpost Talarn Thranta speeder point, which are both very close, and you can cheat a bit by jumping over some mountains to the west and you’ll practically be there.
Big Map of Alderaan for MGGS, with Republic names:
Exact Location of MGGS on in the Juran Mountains, look for the vendor symbol on the map:
Quick Travel / Taxi
Walk to the Corellia Museum
The Corellia Museum is located in the very bottom middle of the Axial Park map, and you’ll want to walk in and take the elevator up.
Upstairs, there is a shuttle, but we won’t be taking the shuttle. Jump up onto the shuttle and onto the shuttle’s wing, so you can jump on the outer ledge of the room.
From there, one of the corners of the ledge has another ledge far down below. Jump down to that ledge.
Follow that wide ledge for a short walk and keep your eyes up. Eventually you will see a glowing blue square up high on the base of a statue above you. If you have the MGGS you will be able to right click that blue square.
From there you will be able to easily jump up to another nearby platform ledge, and walk into a building entrance, and the matrix shard is at the end of a tunnel on top of a shipping crate!