The most common and most likely answer to this crossword clue is the 10 letter word ACCURATELY
I've seen this crossword clue in The Daily Telegraph
A
C
C
U
R
A
T
E
L
Y
Buddy explains!

The straight part
We know that "without any slips" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case without any slips = accurately.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.
What does ACCURATELY mean?
ACCURATELY adverb- In an accurate manner; exactly; precisely; without error or defect.