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Nearly all characters on Brawl can be unlocked in Vs. Mode simply by completing a high enough number of Vs. Battles. The following is the list of how many battles you need to unlock each character.

5:      Ness
10:    Marth
15:    Snake (All 15 must be on Shadow Moses Island)
22:    Luigi
50:    Falco
70:    Captain Falcon
100:  Lucario
130:  Snake (If not on Shadow Moses Island)
160:  R.O.B.
200:  Ganondorf
250:  Mr. Game & Watch
300:  Sonic
350:  Jigglypuff
400:  Toon Link
450:  Wolf
 

Remember, you cannot unlock Ness with just Vs. Mode battles. You must do 5 battles AND meet him in the Subspace Emissary before you can unlock him. He will not appear until both requirements have been met.

Vs. Mode is the method that takes the longest, but also requires the least effort. If you have more time than skill, just do a whole lot of battles and let the challengers come to you.

The Quick Way: If you want to rack up a lot of battles very quickly, set up games that will end as quickly as possible. I prefer stock battles set to 1 life. Then I set it to Sudden Death mode so almost every good hit will do an instant kill. I set up items to the max number of anything highly explosive or long range that will instant kill someone on Sudden Death. With this setup, you can finish a battle in about 10 seconds and start another battle about 10 seconds later. Racking up a battle every 20 seconds will get you done earning R.O.B. in about an hour. Game & Watch will take about one and a half hours. Wolf will take the longest, clocking at about two and a half hours. If you have the patience to do this nonstop for two and a half hours, you can unlock all the characters without much real effort.

Thanks for this guide, but I have just a few corrections.  You don't need to meet Ness in SSE to unlock him.  I unlocked him after I played five Brawl matches, and I had not even started SSE.  Unlocking all of the characters through Vs. mode is actually very quick.  I think that this is even faster than SSE.  I have already unlocked all of the characters, except for Wolf.  If you are really in a hurry to unlock all of the characters, do a special brawl.  Set the game to stamina, and put flowers on the characters' heads.  Then, set your opponents health to 1.  After that, you just keep pressing start, and you can get through a bunch of matches really quickly.  When the match starts, your opponent will immediately lose.  This way is a lot quicker that doing 1 stock sudden death matches.  I hope these tips helped.

Thanks for reminding me. I just fixed it. I corrected it in the Unlock Ness post, but forgot I still had it here. I was pleasantly surprised when I learned Ness was just a 5 battle unlock. I thought I was going to have to go play hours in SSE to get him but there he was jumping out and attacking me after just a few battles. It seems most of the information available online isn't totally accurate. So it's good that we're in here posting stuff we know is correct. Congrats on unlocking the characters. That's awesome that you were able to do it so fast.