You shouldn't stay up late at night.

Literal

Night late [until-まで] being-awake [condition-ては] no-good [assertion-よ].

~てはだめ is the colloquial version of ~てはいけない — だめ (no good) replacing いけない. Common in spoken Japanese and in talking to children. 起きている means 'be awake, be up' (not 'be up and doing things' which would need context). The final よ softens the command with personal involvement.