Player 1 has Ravenbloom Student on Ravenbloom Conservatory, Player 2 enters to that battlefield with empowered Akali, Deadly Weapon, empowered—when she moves she deals 2 damage to Ravenbloom Student, P1 doesn't react. Will Player 1 get defend trigger from the battlefield or not?

No, Player 1 does not get the defend trigger from Ravenbloom Conservatory.

Here's the sequence: Player 2 moves Empowered Akali to Ravenbloom Conservatory (controlled by Player 1, with Ravenbloom Student there). The move completes and Contested is applied. During the following Cleanup, Akali's "When I move" trigger is finalized and placed on the chain, resolving to deal 2 damage to Ravenbloom Student. In the next Cleanup, Ravenbloom Student (2 Might, 2 damage) is killed in step 3b — before step 7 checks for opposing units to stage Combat. Since only Akali remains, no Combat is staged; instead a Non-Combat Showdown begins.

"Defend" in Riftbound is a Combat concept tied to gaining the Defender designation (Rules 383.4.f, 459.2.b.2). Without opposing units present, Combat never stages, Player 1 never becomes the Defender, and Ravenbloom Conservatory's "When you defend here" condition is never met. Player 2 will win the Non-Combat Showdown and Conquer the battlefield.