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She paints every day no matter how busy she is.
Literal
She [topic-は] however busy [even-ても] every-day picture [object-を] writes.
どんなに~ても is the concessive 'no matter how X / however X.' Combined with the i-adjective te-form 忙しくても ('even if busy'), it gives 'no matter how busy she is.' Note the use of 書く ('write') with 絵 ('picture') — this is an old usage that some style guides flag as nonstandard, where 描く (also read かく) is the prescriptive verb for drawing or painting. Modern usage often defaults to 描く for art, but 書く survives in casual writing and traditional contexts; both are read かく.