you can only get one because you chose 1 either it is the arc , void or sol sword. After that Shaxx will get you a quest that tells you , you should kill 50 majors and 25 guardians , after you do that , he will tell you to get to the asylum to kill Echtar the sword of oryx , anyways to open the doors of the asylum will require maybe you can call it a trick , when you face the 3 knights before entering the asylum ( i think at the Founts) you have to kill all of the 3 in 1 super , so you can use a tactic which is to get their health low first , and then use your super to kill them all. Then you will face Echtar , there is a shield on him , so you have to take it out first by the sword , so make sure you have ammunition or you won't hurt him.
Then he will require from you to gather some materials and get 500 kills depending on your weapon element ( void,arc,solar ability kills). it will take time from you especially gathering the materials. How to get the materials
I only got the arc sword , so to get it the materials are on earth , you will have to find 10 zeptocytes . you will find them with the spinmetal,it will be easy to farm the spinmetals but it will take some time from you because the drop rate is like 5-10% i did a video but i haven't uploaded it yet, but i found a video on youtube that a guy shows you how to farm them easily.
for the sol blade it will require to get the solitron flare they will be found with the helium filaments and for the void blade you will find them in relic iron ( can't remember the name).
after that you will to talk to shaxx again and he will tell you to wait until the armsday which is wednesday.
finally he will give you the last step of the quest which is to do a lv42 strike The Sunless Strike
to get the blade is kinda tricky
when you get to to the Alak-hul the darkblade . 1st if you are an arc sword user ( like me ) do this and you will get it, kill the solar and void knights 2nd get alak-hul health too low 3rd kill the arc knight 4th kill alak-hul as fast as you can because you will have to kill him in 30 seconds after killing the arc knight.
thanks guys for reading hope you find this guide helpful in anyway , if you have more tips just tell me because it will benefit everyone. P.S i read that your sword must be above 280 dmg to complete the last step.