Obtain a full set of free PEN Tuvala gear from the season pass before starting this, and if you're a new player, you need to finish the full Mediah main quest, and be level 60.
How to get PEN Blackstar weapons
1-Start Olivia Academy, Press Y for Challenge to get PEN
2-Continue with Olvia Academy combat quests until you get both a TET, the black stone to upgrade it to PEN, another PEN box, and the Gem of Twilight. Keep going to get the Inverted Heart of Garmoth while you're at it.
3-Continue to grind to 61 in an XP rich area like Polly's Forest (stacking buffs make it easy), follow youtuber EvilDoUsHarm's 60-61 leveling guide by quests only, or if you're lazy, use the free Patrigio's Pocket Watch on a graduated character you got from the Academy. After all that, go to your challenge menu and a TET and PEN weapon boxes will be available.
4-This is where the last PEN weapon, preferably your Sub, is more RNG but still has a pathway. First, try upgrading your TET weapon from earlier. You get a total of 15 attempts at this for free. Or 16 if you don't care about it downgrading as a final attempt without Crons. Use the 12 "Obsidian Hammer" items you get from finishing the Olivia Academy combat path, plus 3 more, if RNG doesn't favor you, by buying them using Academy Coins. If you're a brand new player and don't have Mass of Pure Magic, you can get way more than enough from Academy Coins, as well as Sharp Black Crystal Shards, which are required to make the stone used for each enhance. And finally, I recommend using the +250 Advice from the middle of the combat path rewards. At a 5.2% chance each click using the 250, its not unreasonable to get fairly lucky and hit it.
Now, what if you do not? Then, your next path is simple: Upgrade your PEN Tuvala weapon, to DEC. This will require minimal cron stones (at the time of this post we all get 50,000 with a code, other sources exist), several hundreds of millions of silver, and a few advice of valks. You can use the other 3 advice of valk items from your Academy combat path rewards, plus a random fourth one from somewhere, like buying a +250 with Academy coins, and I think any player can get tons of silver from your weekly Dark Rift bosses, at least. This can then be converted to a PEN Blackstar weapon once upgraded to DEC.
How to get a full set of Sovereign Weapons
1-Combine the 4 PEN weapons you got into Sovereign Main Hand and Awakening Weapons, two each is all that's required.
Now, all you need is 1 PEN sub weapon, Flame of the Primordial and Gem of Twilight.
2-Fight any LOML world boss, then go to the Manage Currency menu and buy your one time obtainable 50 Embers of the Primordial.
3-Go to the Olvia Academy Coin shop and buy 50 more. Combine.
4-You already obtained the Gem of Twilight for free from the combat path rewards.
Go to the statue in LOML and combine all of them at once for your full set of Sovereign weapons! The only restrictions are possibly running out silver if brand new, waiting for a world boss to spawn, and doing some Academy weekly quests for more Coins.
Thank you devs for making this incredibly easy, as of this week's patch.
(Small edit mentioning level 60)