The answer is simple. Bitcoin is like the king of crypto world. When the king is strong and prosperous, his kingdom is also happy. Trade flourishes, new people settle in etc. But when the king is weak and has a declining health, then the effects are visible in his kingdom too. Trades become less, people start moving out etc.

Currently Bitcoin is the focus point of crypto world and represents the trust in cryptocurrencies. It is also the gateway to crypto world and is paired against the maximum number of cryptocurrencies. So when Bitcoin's prices go down, people basically lose trust in cryptos, and start selling their altcoins too; thus bringing the price of altcoins down.

As for which altcoin can escape this cycle, then the answer is probably none.