We study an adversary who attacks a Proof-of-Work (POW) blockchain by selfishly constructing an alternative longest chain. We characterize optimal strategies employed by the adversary when a difficulty adjustment rule alà Bitcoin applies. As time (namely the times-tamp specified in each block) in most permissionless POW blockchains is somewhat subjective, we focus on two extreme scenarios: when time is completely verifiable, and when it is completely unverifiable. We conclude that an adversary who faces a difficulty adjustment rule will find a longest-chain attack very challenging when timestamps are verifiable. POW blockchains with frequent difficulty adjustments relative to time reporting flexibility will be substantially more vulnerable to longest-chain attacks. Our main fining provides guidance on the design of difficulty adjustment rules and demonstrates the importance of timestamp verifiability.