Just like other members mentioned, you should use proper bitcoin mixing service with great reputation. But, i also suggest you to use exchange (or instant exchange) to swap your bitcoin with anonymous cryptocurrency (such as Monero) and then sell the anonymous cryptocurrency for bitcoin at other exchange
Instant exchanges save all data, which isn't really the case with mixers since they destroy all data after a certain period of time. Whether or not they really delete all user information is subject to a different discussion, but that at least is the intention. Another thing is that when you sell your Monero at whatever other exchange, you again leave data behind, which isn't something you want to happen in case you strive for the highest possible form of 'anonymity'. On top of that, with all the regulations going on, I don't think these 'instant' exchanges will allow people to exchange one crypto for the other without verification endlessly -- at some point it's going to stop.
To add on, It'll be more expensive if you use such alternative because of multiple deposit/withdrawal (miner fee) and trading fee's, furthermore the bitcoin network is still congested up until now so every on chain transaction requires a high miner fee (compared than usual).
Meanwhile if use an actual mixing service, you will only need to pay for the miner fee of a single deposit and withdrawal as well as the mixing fee.
In chipmixer's case, you can withdraw through private keys so you can just import it into another wallet to avoid another miner fee.
ANN thread:
https://bitcointalk.org/index.php?topic=1935098.0