Correct spelling for the English word "shakest" is [ʃˈe͡ɪkəst], [ʃˈeɪkəst], [ʃ_ˈeɪ_k_ə_s_t] (IPA phonetic alphabet).
The word "shakest" is an archaic form of the verb "shake", specifically the second person singular indicative present tense of "shake" in Early Modern English. It comes from the Old English verb "scacan" or "sceacan". Over time, the conjugation of this verb changed, and "shakest" became obsolete in modern English, where we use "shake" for all persons in the present tense (I shake, you shake, he/she/it shakes, we shake, you shake, they shake).