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LingakuLingakuのが下手 means "bad at doing". The verb is in the dictionary form, の turns it into a noun, and that noun takes が before 下手. The person who is bad at it takes は.
The verb stays in the dictionary form when the sentence is in the past; only 下手 changes. 下手 is a な-adjective: へた下手だった, へた下手じゃない.
English "bad at" pulls learners towards を, and the の is easy to drop.
下手 says how well something is done. にがて苦手 says you find it hard or don't like it, and it is the gentler word for your own weak points. Calling someone else 下手 to their face is blunt.
With a noun, there is no の: りょうり料理がへた下手です. The opposite is のがじょうず上手.