"连续左右猛击" can be translated as "repeatedly pounding left and right" or "delivering a series of forceful left and right strikes" in English, depending on the context.
If describing an action in a general or literal sense (e.g., in sports, combat, or a physical activity), "repeatedly pounding left and right" is a straightforward choice.
If emphasizing the intensity or forcefulness of the strikes (e.g., in a more vivid or dramatic context), "delivering a series of forceful left and right strikes" might be more appropriate.
Choose the phrase that best fits the specific context you're working with.