In a theoretical Casper bribe attack, an attacker has enough resources to offer conditional bribes to other validators that incentivize them to validate a deviant chain. An attacker would have to pay security-deposit-sized bribes to a majority of validators to revert the chain. This gives Casper PoS a security advantage compared with a PoW protocol facing a similar bribing attacker. The extreme cost makes it practically impossible for a bribing adversary to acquire enough validator node keys to take control of the blockchain.
Attacking an individual shard is theoretically similar to attacking the main chain, though much easier with currently proposed sharding protocols. This is a challenge currently being addressed by Ethereum PoS researchers and developers.