Can Akali, Silentbe chosen and killed by Singularity?

Yes, Akali, Silent can be chosen by Singularity — but only if she is in combat.

Akali's ability says she can't be chosen by enemy spells and abilities unless she's in combat. Singularity deals 6 to each of up to two units — it targets those units (Rule 355.6–355.7).

• If Akali is not in combat: She is an illegal target for Singularity. You can't choose her.
• If Akali is in combat: The exception kicks in. Singularity can target her, and if it resolves, 6 damage kills her (she has 4 Might — lethal damage, Rule 428.1.a.2).