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I think Big Bird scales to at least Kermit the Frog in terms of durability. Considering how Big Bird is considerably bigger than Kermit, and that Kermit has survived an explosion and being shot with cannon balls, I would say that Big Bird would probably survive the Space Shuttle Challenger disaster explosion. Also, I think it's reasonable to assume that Big Bird would survive impact with the Atlantic Ocean while traveling at terminal velocity. From there he could just tread water until rescue arrived or swim to shore. Which ever is quicker.

VS Battles Wiki page Kermit the Frog