There are five datacrons on the Republic faction version of Taris. The blue and orange mastery datacrons require some finesse with platforming, the matrix shard requires assistance from another player, while the other two are quite easy to get. They provide minimal attribute bonuses and one matrix shard. All five are required for the Taris Datacron Master (Republic) achievement.
The Republic Taris +2 blue mastery datacron.
Codex type: Achievement: Datacrons
Codex location: Taris: Republic Resettlement Zone
Codex coordinates: -1513, -254
Faction: Republic
Class: Jedi Consular - Jedi Knight - Smuggler - Trooper
Associated Achievement: Taris Datacron Master (Republic)
The Republic Taris +2 orange mastery datacron.
Codex type: Achievement: Datacrons
Codex location: Taris: The Tularan Marsh
Codex coordinates: 1047, 454
Faction: Republic
Class: Jedi Consular - Jedi Knight - Smuggler - Trooper
Associated Achievement: Taris Datacron Master (Republic)
The Republic Taris +2 red mastery datacron.
Codex type: Achievement: Datacrons
Codex location: Taris: The Tularan Marsh: Transport Station 5
Codex coordinates: 1186, -574
Faction: Republic
Class: Jedi Consular - Jedi Knight - Smuggler - Trooper
Associated Achievement: Taris Datacron Master (Republic)
The Republic Taris +2 red mastery datacron.
Codex type: Achievement: Datacrons
Codex location: Taris: The Sinking City: Dynamet General Hospital: Emergency Exit
Codex coordinates: -363, -227
Faction: Republic
Class: Jedi Consular - Jedi Knight - Smuggler - Trooper
Associated Achievement: Taris Datacron Master (Republic)
The Republic Taris green matrix shard datacron.
Codex type: Achievement: Datacrons
Codex location: Taris: The Tularan Marsh: Abandoned Power Plant
Codex coordinates: 1060, 1038
Faction: Republic
Class: Jedi Consular - Jedi Knight - Smuggler - Trooper
Associated Achievement: Taris Datacron Master (Republic)
Special Requirements: This requires cooperation between two players. One will need to activate the computer console to blast the other player into the pipes overhead. The angle the air jets push a player at are random so it may take several tries to land on the pipes.