You don’t need to use an alt.

If you do the two guaranteed token-drop dailies (“Barking” & “This One Time, When I Was Drunk”) you’ll get 25 tokens. You can also do “There and Back Again” every eighteen hours. That one yields a variable number of tokens, but you should easily get ten per day. I did it this morning and even with getting the exhaustion debuff once earned eighteen tokens. After another day of practice I expect to be getting in the mid-20s easily. Be aware that there’s no exclamation mark indicating a questgiver for this one. You just talk with the NPC who gave you your original keg delivery quest to start it each time.

There are thirteen days left in the event, so assuming you earn forty tokens a day (and ignoring the 40 for “Pink Elekks”, 10 for “Now This is Ram Racing…Almost”, 10 for “Chug and Chuck”, and 40 for “Saving Brewfest”) you’ll have no problem getting enough for the meta achievement. Forty per day should be very easy, particularly if you’re aggressive about the eighteen hour reset on Ram Racing. If you return some or all of your Brewfest gear after completing “Disturbing the Peace” before signing up for Brew of the Month Club as recommended by Drew, you’ll be done even sooner.