To answer this question, it is helpful to begin at the end of the phrase.
The noun is manner. What kind of "manner"
is it? A friendly manner [adjective (friendly) + noun
(manner)]. Note that "friendly" is an adjective even though
it ends in -ly.
In what way is it friendly? It is environmentally friendly
[adverb (environmentally) modifying an adjective (friendly)]. So, the
correct phrase is environmentally friendly manner,
#3 in your list above.
There's one other possibility, although this would be rather unusual.
If you change the modifiers to a single unit (by adding a hyphen), you
could possibly say an environment-friendly manner (noun-adjective
combination), #2, but modified, in your list above. However, most people
would use and understand environmentally friendly manner
much more easily.
#1, Environmental friendly manner, is neither a logical
nor meaningful phrase.