This study uses high-frequency (1-min) price data to examine the connectedness among the leading cryptocurrencies (i.e. Bitcoin, Ethereum, Binance, Cardano, Litecoin, and Ripple) at volatility and high-order (third and fourth orders in this paper) moments based on skewness and kurtosis. The sample period is from February 10, 2020, to August 20, 2022, which captures a pandemic, wartime, cryptocurrency market crashes, and the full collapse of a stablecoin. Using a time-varying parameter vector autoregressive (TVP-VAR) connectedness approach, we find that the total dynamic connectedness throughout all realized estimators grows with the time frequency of the data. Moreover, all estimators are time dependent and affected by significant events. As an exception, the Russia–Ukraine War did not increase the total connectedness among cryptocurrencies. Analysis of third- and fourth-order moments reveals additional dynamics not captured by the second moments, highlighting the importance of analyzing higher moments when studying systematic crash and fat-tail risks in the cryptocurrency market. Additional tests show that rolling-window-based VAR models do not reveal these patterns. Regarding the directional risk transmissions, Binance was a consistent net transmitter in all three connectedness systems and it dominated the volatility connectedness network. In contrast, skewness and kurtosis connectedness networks were dominated by Litecoin and Bitcoin and Ripple were net shock receivers in all three networks. These findings are expected to serve as a guide for portfolio optimization, risk management, and policy-making practices.