If you are the kind of player that isn’t interested in ranked pvp or hardmode/nightmare raiding, you may be finding it relatively tedious to grind up your gear rating through Legacy of the Sith, let alone upgrading colour quality from Green to Purple.
There is a really fast method that many end-game players have been speeding through in order to get started with playing harder content.
332 Thrysian Purple gear has the same stats as R-4 Hardmode Purple 340 gear when inside PvP Instances.

Essentially, once you have obtained your 2 Legendary Set Implants, you only need to worry about the remaining 12 slots. If you’re a Tank or a Healer, you don’t even need to worry about the accuracy stat.

Let’s quickly go over how this works. Flashpoint, PvP and Raiding [WEEKLY] quests give you a box (pictured above) that gives you an “assured” upgrade based on a piece of lowest-quality gear. However if you aren’t a raider or an avid PvPer, the grind for Purple quality gear may seem daunting.

PvP has the highest valued colour-quality at 332 which gives Purple without raids.
Simply put, once your 2 Legendary Implants are equipped you have 12 slots that need filling with the best gear you can grab. If you don’t have 2 Legendary Implants, the game will also give you Implant-item rewards which are a waste of upgrade effort.

My suggestion is to HOLD onto your PvP based Thrysian Requisition Caches. You can obtain 3 a week (per character) from both the GSF weekly and the PvP Warzone weekly, aka 6 a week per character. Before Arenas.
Ergo you can obtain all necessary 12 boxes by doing all weeklies on 2 characters (of the same adv class) in 1 week or over 2 weeks with 1 character.

Now here comes the grind, play your flashpoints (complete the Weekly) and unbox PvE caches or pay to upgrade to get the items to a 324 (not 326) rating. Your 2 Legendary Implants are already 330 (or higher) so they are safe. If you have left over Aquatics and Medals of Commendation I suggest buying Conquest-based green Decurion gear to 330 as makeshift gear to quickly replace.

Alternatively through your 12 PvP box grind, PvP should give enough Thrysian currency to buy multiple starting PvP gear from fleet and upgrade to 332 or 330 directly (Takes about 260 Thrysian from 318 to 326).

Once all slots are 330 except your Legendary Implants, Open 1 single Thrysian box, and then equip that Purple 332 onto your character. Then open another, equip, so on and so forth…

Keep in mind as Thrysian is PvP based your DPS gear will not have accuracy inserted. However as your gear is Purple 332, play some Flashpoints and eventually you will receive natural 332 drops that contain accuracy as needed. You won’t have to rely on buying or upgrading from [WEEKLY] boxes.

Purple 332 Gear even without DPS accuracy is good-enough, sometimes overpowered for:
All future story content in 7.0 – Overpowered
All Daily and Heroic areas – Overpowered
PvP Arenas – Good-Enough
All Difficulties of Flashpoints – Sometimes Overpowered
All Story Operations – Overpowered
All Difficulties of Uprisings – Good-Enough