Null Space BFR is not instant. It's main way of getting people in is sucking people in via wind, like airlocks in space.
The Avatar's grappling hook (A very durable and bullshit one, yet still a grappling hook) could resist the winds for a few seconds, and Tails was also resisting the pull.
Gim could prevent getting into Null Space the same way, considering how he literally resists black holes on his page.
Although, Illusions still work on robots as seen with Shadow and Forces: Speed Battle, but I'm pretty sure the votes for Infinite shouldn't count. Infinite doesn't even BFR in-character anyways, Eggman told him to
In-character, Infinite either retreats while attacking the opponent giving chase with Illusions in wide areas, or trying to land an Illusion hit to mess up the opponent in smaller areas.
I'm assuming this is the Death Egg from Sonic 2 and NOT Forces as it's labeled "Death Egg Zone", so Infinite will try to constantly try send Gim into Illusion Mode. It varies on who has higher AP since this would literally just be a normal Kirby boss