The Destroyer's "Possible Flight"

[XSpuky9]

On its profile it is listed that The Destroyer has "Possible Flight".

The Destroyer shoudn't have Flight. It has a modified version of the Worm AI ("Similar to worm AI except it will shoot projectiles from the body and tail and is unable to "fly" in air. It will also release Probes.", quote from the Terraria Gamepedia) which can freely move trough solid blocks, ignoring knockback and liquids, but it can move like this only if it touches blocks, meaning that if you build a bridge in the sky, The Destroyer won't reach it because it needs to grab on to blocks and it can only jump to a certain height. It will attempt to fly (jump) in from below and touch the bridge.

This means that The Destroyer can't battle in a space with no blocks to dig trough (like outer space). In other worlds, it can't fly.

 

[Overlord775]

from the official terraria wiki "When The Destroyer is off-screen it can move around freely, as though it were moving through blocks, even through the air"

 

[Saikou_The_Lewd_King]

As stated above, the Destroyer can "fly" if offscreen.