Do you have to complete mgs4 on the boss extreme to get the big boss emblem

Yes. The requirements for the Big Boss Emblem are;

The Boss Extreme Difficulty
0 Alerts (Cautions are ok)
0 Continues (no deaths)
0 Special Items (i.e. bandana, stealth)
0 Recovery Items (rations, regain, etc.)
0 Kills [(B&B Corps Included) Unmanned weapons excluded]
Under 5 hours of game play (scenes and credits are considered game play)

You will get the BBE and the Big Boss Face Camo (actually Solidus)