下列还有三个短语相同意思:
cook up a storm烹饪上露一手
dance up a storm舞姿翩翩
talk up a storm 侃侃而谈
[MAINLY US INFORMAL:主要用于美国,非正式用语]
to do something with a lot of energy and often skill:[以非凡的能力和技能做某事]
Rob was in the kitchen cooking up a storm.
Rob在厨房里大显身手.
(from Cambridge Advanced Learner's Dictionary)
sing up a storm,大显歌喉翻译根据情况而定吧,供参考而已.