The most common and most likely answer to this crossword clue is the 6 letter word CRACKS
I've seen this crossword clue in The Times
C
R
A
C
K
S
More clues leading to the result CRACKS
Buddy explains!

The straight part
We know that "Attempts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case attempts = cracks.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 CRACKS mean?
CRACKS noun- A thin and usually jagged space opened in a previously solid material.
- A narrow opening.
- A sharply humorous comment; a wisecrack.
- Crack cocaine, a potent, relatively cheap, addictive variety of cocaine; often a rock, usually smoked through a crack-pipe.
- The sharp sound made when solid material breaks.
- Any sharp sound.
- A sharp, resounding blow.
- An attempt at something.
- Vagina.
- The space between the buttocks.
- Conviviality; fun; good conversation, chat, gossip, or humorous storytelling; good company.
- Business; events; news.
- A program or procedure designed to circumvent restrictions or usage limits on software.
- (elsewhere throughout the North of the UK) a meaningful chat.
- Extremely silly, absurd or off-the-wall ideas or prose.
- The tone of voice when changed at puberty.
- A mental flaw; a touch of craziness; partial insanity.
- A crazy or crack-brained person.
- A boast; boasting.
- Breach of chastity.
- A boy, generally a pert, lively boy.
- A brief time; an instant; a jiffy.
- To form cracks.
- To break apart under pressure.
- To become debilitated by psychological pressure.
- To break down or yield, especially under interrogation or torture.
- To make a cracking sound.
- (of a voice) To change rapidly in register.
- (of a pubescent boy's voice) To alternate between high and low register in the process of eventually lowering.
- To make a sharply humorous comment.
- To make a crack or cracks in.
- To break open or crush to small pieces by impact or stress.
- To strike forcefully.
- To open slightly.
- To cause to yield under interrogation or other pressure. (Figurative)
- To solve a difficult problem. (Figurative, from cracking a nut.)
- To overcome a security system or a component.
- To cause to make a sharp sound.
- To tell (a joke).
- To break down (a complex molecule), especially with the application of heat: to pyrolyse.
- To circumvent software restrictions such as regional coding or time limits.
- To open a canned beverage, or any packaged drink or food.
- To brag, boast.
- To be ruined or impaired; to fail.