To a very great extent (8)
<span class="explanation-format__ClueExplanation">'<span class="explanation-format__original">to a very great extent</span>' is the definition.<br/ ><span class="explanation-format__explanation">(I've seen this before)</span><br/ ><br/ >This is all the clue.<br/ ></span>
(Another definition for mightily that I've seen is " To a very great extent".)
(Other definitions for by far that I've seen before include "To a superlative extent" , "Very much" , "easily" .)