Besides many reasons mentioned above to eliminate optins C D and E, one more reason is that..
One must not use a progressive tense for a future action unless it is absolutely necessary. Hence C D and E can be ruled out.

Between A and B its straight A for paralellism.

Many environmentalists believe that the widespread planting of trees, along with the conservation of existing forests, would be one of the surest, easiest, and least expensive ways to begin to halt or even to reverse the buildup of carbon dioxide in the air
(A) one of the surest, easiest, and least expensive ways to begin to halt or even to reverse :

........Planting of trees would be one of the ways to begin........ to halt X.......OR........to reverse X ( Perfect Parallelism ),

furthermore usage of would/ future course of action ----- best is to pair it up with an Infinitive, as correctly done in A

(B) one of the most sure, easy, and least expensive ways to begin a halt or even reverse : superlative Least incorrectly paired with sure / easy --- Eliminated

(C) one of the surest, easiest, and least expensive ways that would begin halting or even reversing

usage of would demands the infinitive form , lets rewrite this

........ Planting of trees would be one of the ways THAT begin halting or reversing X ( does it make sense? / Can this outweigh option A ) ---- Eliminated

(D) a most sure, easy, and inexpensive way beginning the halting and even reversing of : ( a most sure way --------raises eyebrows ) ---- Eliminated

(E) the most sure, easiest, and inexpensive way that would begin halting or even reversing : incorrect usage of most sure ( superlative easiest is incorrectly paired up with most sure / inexpensive ) ---- Eliminated

leading to A , my take

Planting of (Complex gerund) parallel with conservation of (action noun), hence structurally it should be parallel with Halting of and reversing of. So why not C?