The most common and most likely answer to this crossword clue is the 3 plus 3 plus 2 plus 5 letter word ITS NOW OR NEVER
I've seen this crossword clue in The Guardian
I
T
S
N
O
W
O
R
N
E
V
E
R
Buddy explains!
The straight part
We know that "This is our last chance!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this is our last chance! = its now or never.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.