To acquire the emblem "whenever a creature you control deals combat damage to a player, that player loses" does Vraska have to remain alive? other words can I cast vraska with its 4 loyalty counters activate the -9 effect killing vraska off & acquiring the emblem?
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When Vraska's last ability resolves, "you" will get the emblem even if Vraska isn't on the battlefield anymore (because the ability exists independently of Vraska) (C.R. 113.7a). Likewise, the emblem's ability will trigger as appropriate even if Vraska isn't on the battlefield anymore.
Thus, for example, if Vraska has exactly nine loyalty counters on her, you can activate her last ability (not: effect) (C.R. 606.4), she goes to the graveyard (C.R. 704.5i, 306.5c; see also C.R. 306.5), and the ability will still get to resolve (C.R. 113.7a). (To be clear, you can activate a permanent's "-N" loyalty ability only if that permanent has N or more loyalty counters on it [C.R. 107.7, 118.3, 602.2, 602.2b, 601.2h]. For example, you can't activate Vraska's last ability if Vraska has only four loyalty counters on her.)
Vraska, Golgari Queen other words can I cast vraska with its 4 loyalty counters activate the -9 effect killing vraska off & acquiring the emblem?
No, you can't.
Vraska needs at least 9 Loyalty counters for you to activate its ultimate ability: the cost is 'remove 9 counters'; if there are only 4, you simply can't pay the cost, thus can't activate the ability. (rule 606.5)
But, yes, if Vraska has exactly 9 counters, you can activate it; and Vraska will die immediately, but you'll get the emblem.