AHOY M8TY. SPOILERS AHEAD
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Subspace emissary is not on the Single Layer release of brawl. So here is the list on how to unlock without playing SSE
Through Brawling (VS mode) [Number of VS fights needed]
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Ness 5
Marth 10
Luigi 22
Falco 50
C.Falcon 70
Lucario 100
Snake 130
R.O.B 160
Ganondorf 200
Mr.Game and Watch 250
Sonic 300
Jigglypuff 350
Toon Link 400
Wolf 450
Non SSE/Classic
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Falco - Multiman Melee (100 man melee)
Ness - Reflect 10 shots
Snake - Play on shadow moses island for 15 times
Mr Game and Watch - Beat break the target level 1 with over 30 characters
Sonic - Play VS 15/20 hours (not sure, but got him after playing about this long)
Break the Targets
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For Break the Target unlocks
2&3 - play classic on 2nd difficulty and quit at stage 11
4&5 - play classic on 4th difficulty and quit at stage 11
Lv2 Beat classic mode with easy TWICE, or beat it with normal ONCE.
Lv3 Beat classic mode with normal TWICE, or beat it with hard ONCE.
Lv4 Beat classic mode with hard TWICE, or beat it with very hard ONCE
Lv5 Beat classic mode with very hard TWICE.
Events
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Missions 21 - (28 to 30) Beat events 1 - 20 and have R.O.B unlocked
Missions (29 to 31) - 40 Beat all the remaining events and have everyone unlocked
Mission 41 - Beat mission 40
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Subspace emissary is not on the Single Layer release of brawl. So here is the list on how to unlock without playing SSE
Through Brawling (VS mode) [Number of VS fights needed]
-----------------------------------------------------
Ness 5
Marth 10
Luigi 22
Falco 50
C.Falcon 70
Lucario 100
Snake 130
R.O.B 160
Ganondorf 200
Mr.Game and Watch 250
Sonic 300
Jigglypuff 350
Toon Link 400
Wolf 450
Non SSE/Classic
------------------------------------
Falco - Multiman Melee (100 man melee)
Ness - Reflect 10 shots
Snake - Play on shadow moses island for 15 times
Mr Game and Watch - Beat break the target level 1 with over 30 characters
Sonic - Play VS 15/20 hours (not sure, but got him after playing about this long)
Break the Targets
------------------------------------
For Break the Target unlocks
2&3 - play classic on 2nd difficulty and quit at stage 11
4&5 - play classic on 4th difficulty and quit at stage 11
Lv2 Beat classic mode with easy TWICE, or beat it with normal ONCE.
Lv3 Beat classic mode with normal TWICE, or beat it with hard ONCE.
Lv4 Beat classic mode with hard TWICE, or beat it with very hard ONCE
Lv5 Beat classic mode with very hard TWICE.
Events
-----------------------------------------------------
Missions 21 - (28 to 30) Beat events 1 - 20 and have R.O.B unlocked
Missions (29 to 31) - 40 Beat all the remaining events and have everyone unlocked
Mission 41 - Beat mission 40