The phrase "didst on sly" is an archaic way of saying "did it secretly" or "did it covertly". Some synonyms for this phrase might include "did it surreptitiously", "did it furtively", "did it stealthily", or "did it clandestinely". All of these phrases essentially mean the same thing: that someone did something in a way that was meant to remain hidden or unknown to others. Other synonyms might include "did it on the down-low", "did it on the sly", or "did it in secret". Ultimately, all of these phrases convey a sense of sneaking around or doing things behind others' backs.