Well, Amelia has Acausality Types 3 & 4, meaning she's gonna back because of other versions of herself AND she operates on a different system of cause & effect, making interacting with her difficult. (The former is probably also why she has Immortality Type 4. That & her claiming she respawns)
Her Type 8 Immortality is reliant on... her true form? Which is also the basis of her Type 9 Immortality?
Since she has the Infinity Gauntlet, she has flat out Omnipresence for being everywhere & everything, apparently, albeit, this was never directly demonstrated & was for a different character, but she still has it. It also means she has Nigh-Omniscience because The Infinity Stones were stated to grant the user Omniscience, & Power Nullification.
Meanwhile, Bugs HAS Acausality, too:
Causality Manipulation (
Granted and undid a wish that altered history), possibly
Acausality (Was unaffected by that wish and
like Wile E. Coyote should be unaffected from having a previous page of his own story altered)
....but it seems to be Type 1, which is just Time Paradox Immunity. Not as useful as Type 3 or 4.
Bug's Immortalities are Types 1, 3, 4 & 8 (
At 13:37, it is said that Bugs doesn't age and stays young as long as people still laugh at him and his cartoons.
Made a grim reaper/rabbit give up to the point he doesn't want Bugs' soul anymore),
Not aging & staying young & a grim reaper not wanting your soul probably aren't enough. Good thing his Type 3 is based on Mid-Godly, I guess.
He has Dimensional Travel, but Unknown Range with it, so BFR-ing him MIGHT not work?
Would Sealing work, or he could Dimensional Travel/Immersion out of it?
Bugs SEEMS to have Resistance to Transmutation, since it's listed twice, & 1 of them is after a "Resistance to" with some stuff between it, but there isn't a justification, so I dunno the potency of the Resistance.
He has Resistance to Mind Manipulation, but no Justification for it.
I don't know if Sana's Crystal Ball Precognition or Bugs's warning himself of incoming attacks/events Precognition is better, but then again, Bugs's might not matter because Acausality, lol.
In theory, she could kill him with a Durability Negating Ame Ame Ha, but Mid-Godly Regen says hi, & if Bugs killed her, another Ame would just take her place.
Also, if she can somehow get him to drink a Watsonian Concoction, it can "take away your soul". I don't know if this will stop Bugs, or if he'll Regen from it.
In theory, Amelia has the better Range, but....
Range: Boundless (No matter where your mom is, she will always find a way to reach and ground pound her)
This might just be a Speed/Skill/Preparation/Intelligence feat, but even as a range feat, it doesn't sound like she'd USE her Range unless someone's mom is involved.
HOWEVER, Bugs only has Superhuman Stamina. Ame has Limitless. What prevents Bugs from EVENTUALLY just collapsing of exhaustion?
Plus, he can't interact with her as much, due to her Acausality, his range being Unknown -As opposed to a known value that might be enough to affect an Omnipresent character- & due to the Infinity Gauntlet.
Meanwhile, Bugs can't do much due to Acausality Types 3 & 4, she might be able to escape BFR with her Dimensional Travel, if it even works on her, since she's an Omnipresent Acasual, & she's way's smarter, being Nigh-Omniscient, with Limitless Stamina. (But the Omnscience & Omnipresence are via her Infinity Gauntlet, so IDK if she or her other versions would still have it if Bugs took it.)