The fastest way now is to buy it.

You have some options if you would rather pay with your time instead of your money.

You can get Undaunted points for certain achievements that can be farmed in ordinary delves and public dungeons (even at dolmens too), like Dungeon Ruler/Lord and Dungeon Damage Dealer/Healer/Blocker.

You can also get 30 points for completing This One’s on Me, the achievement for buying a drink for an Undaunted member in the 15 base game alliance zones plus Coldharbour.

Those are all one-time-only per character, though, and they will only get you so far.

For repeatable points, you can run Bolgrul’s daily delve quests—if you can get shares, I believe you can do all 15 unique quests per day.

You do get points for completing a dungeon the first time (norm and vet) even if it isn’t the daily, so you can run through them all in a row to get Undaunted rep and a skill point per dungeon.

It’s a long grind any way you look at it, unless you just want to buy it. Depends on what you prefer to do.

Edit: corrected spelling of Bolgrul

Join a guild - most any guild with a lot of active players will have chat call outs throughout the day for people doing the undaunted dailies... and that will be more enjoyable than getting in the queue with the common folk.

If you do veteran pledge, kill all bosses, hardmode, speedrun and no death for dungeon you get 60 undaunted experience points. Do it for all 3 daily pledge dungeons and you are close to 200 given that there are many side achievements in dungeons like clicking all message stones or reading all notes or killing bosses in certain way. So even if you fail no death in certain dungeons which will happen probably, you can still do this fairly reliably.
You need 1300 undaunted experience for skill line lvl 9 at which all passives and active skills are unlocked, so if you do it in this manner you are done in a week of casually playing. Undaunted pledges are really the key here. Out of those 60 xp points, pledge quest actually gives you 20.
You can do the same by spamming dungeons and finishing them without them being pledges but people are less likely to go out of their way to help you that way and you will need to do more dungeons because of no quest experience for pledges.

Don't forget the Undaunted delve dailies, which you can share in groups. Get a big group of people together, have each one take the daily and share it, do it, turn it in, rinse and repeat. If you get lucky without many repeats I believe you can do 15 total every day which is now 150 Undaunted points.

Takes about half a day to get it to max if you focus on vet dungeon achievements, assuming you have a group that is good enough to reliably get most of the achievements in one run.

There's a couple of good tricks involving the daily delve quest:

1) load up every character who is at least level 45 with the quest, then share the quest with a friend, then log into the one you to level, and let you friend share it back to you. Once that quest is completed, do it again with another alt.

2) ask friends and guild mates to get the quest, and share it with you.

3) if you load up all your characters with the quest today, but do them tomorrow, you can tomorrow's quest too, ie double the fun. This works well with (1).

The Undaunted passives don't make or break a PvP character, 6% max resources will make minimal difference so no reason to rush it.