The most common and most likely answer to this crossword clue is the 10 letter word LIFE-BLOOD
I've seen this crossword clue in The Times
L
I
F
E
-
B
L
O
O
D
Buddy explains!
The straight part
We know that "Julius Caesar’s ultimate loss" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case julius caesar’s ultimate loss = life-blood.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.