The most common and most likely answer to this crossword clue is the 15 letter word PSYCHOBIOGRAPHY
I've seen this crossword clue in The Times
P
S
Y
C
H
O
B
I
O
G
R
A
P
H
Y
Buddy explains!
The straight part
We know that "special sort of life" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case special sort of life = psychobiography.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.