The most common and most likely answer to this crossword clue is the 4 plus 3 plus 6 letter word HALF THE BATTLE
I've seen this crossword clue in The Times
H
A
L
F
T
H
E
B
A
T
T
L
E
More clues leading to the result HALF THE BATTLE
Buddy explains!
The straight part
We know that "big strides towards success" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case big strides towards success = half the battle.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.