My Aisha would like some better equipment for fighting, sure, we both know she can easily take down the Neggbraker, but she finds that battlecards don't do very much damage. What she is asking for is a multiple use weapon that can deal damage. The Neggbreaker's weakness is earth icons, right? Know anything real good and multiple use?

You only need the Amulet you get from the Clockwork Negg to defeat the Neggbreaker. It deals ~20k damage per hit on the Neggbreaker no matter how strong/weak your pet is

I'd like a good healing item though, she doesn't have any on hand, as well as a stealing item.

You don't need any of those items to beat the Neggbreaker.

 

This is my regular battle set:

2 scarab rings (dual duty)

1 honey potion

1 downsize

1 greater healing scroll

1 leaf shield

1 randomly firing freeze ray (snowglobe staff is a good cheaper alternative)

 

for a stealer I suggest purple sticky hand.

TDN's Battlepedia has a good guide on weapon sets here. You don't need any fancy items to beat the Neggbreaker, I literally just beat the guy with a basic pet with just the amulet equipped. But if you're set on buying a healing item, a Lesser Healing Scroll/Greater Healing Scroll will be your best option, and a Purple Sticky Hand for stealing.