Hacking Bitcoin network
It is nearly impossible to hack the Bitcoin network and steal Bitcoins. You will need to find the private key for a particular public address. The possibilities are limitless. Still a group is working on a project to crowd source computation power to find private keys to the Bitcoin network:
“The "Large Bitcoin Collider" (LBC - a homage to ) is a distributed effort to find at least one collision of private Bitcoin keys by creating addresses to private keys in a continuous 2^160 range. These are checked against the list of known BTC addresses with funds on them. In the rare event of a collision, the funds on the address in question would become accessible to the collision finder.”
You can lend the computational power on your computer to help them find the private keys.
They recently managed to open a BTC wallet with 0.54 BTC.
Hacking a Bitcoin exchange
More easier way will be to hack into a Bitcoin exchange. An hack similar to Mt. Gox hack of 2013 will send market into frenzy.
The market will respond negatively to the hack and people will start selling their Bitcoins to safeguard their money.
Triggering panic:
If you just want to create panic in Bitcoin world and let it burn in fire you might have to take number steps. Obviously you will need a group of hackers determined to do this. I would imagine something go like this:
Create a panic in the market that whales are finally selling their Bitcoins. It has reached the bubble stage
Create multiple accounts on the social networks and complain how you are not able to withdraw funds (both BTC and fiat) from the exchanges.
Start spamming the Bitcoin network to create artificial congestion.
Leak the news that few Bitmain miners exploded due to overclocking of the system. The explosion lead to loss of lives and the facility.
Show sponsored news to mobile wallet users. Trick them to click to your website and start tracking the users.
Open a coordinated attacks in public wifi areas, and steal Bitcoins from above users.
Use the pump and dump groups and trick them into buying cheap altcoins and ditch the Bitcoins simultaneously.
Probably a news of top chinese official accepting bribes in Bitcoin will help the cause.
Even after all these, Bitcoin might survive.