The most common and most likely answer to this crossword clue is the 12 letter word CARTWHEELING
I've seen this crossword clue in The Sunday Telegraph
C
A
R
T
W
H
E
E
L
I
N
G
Buddy explains!

The straight part
We know that "performing acrobatics" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case performing acrobatics = cartwheeling.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 CARTWHEELING mean?
CARTWHEELING verb- To perform the gymnastics feat of a cartwheel.
- To flip end over end: normally said of a crashing vehicle or aircraft.