Let's see...
Dialga's most notable powers are:
Transmutation and Matter Manipulation: Neither of this powers will work on Chara, since she is Non-Corporeal/Abstract
Omnipresence: Well, Dialga is only Omnipresent in its own space, while Chara's influence exists in all possible timelines
Causality Manipulation and Time Manipulation: Causality Manipulation won't do nothing to Chara, since she is... Well Acausal, and i think Time Manipulation won't do much to her, all Dialga can do is try to erase Chara's Saves, but its quite obvious that she doesn't need them anymore and the fact that she is Acausal will make Dialga's Time Manipulation useless
Spatial Manipulation and Reality Warping: I think Reality Warping and Spatial Manipulation can be pretty effective on Chara's Incorporeality and Immortality
The Rest: Well, the rest is pretty much useless against Chara, Forcefield is useless against Chara's Omnipresence, Elemental Manipulation... I don't have any idea of what Dialga can do with that...
Chara's powers are:
Immortality (Type 8) and Mid-Godly Regenerationn: Well... Chara's immortality will make her damn hard to kill, but i think Dialga's Reality Warping can affect that, while her Mid-Godly Regenerationn will make her pretty hard to take down too
Possession and Incorporeality: Chara's possession certainly won't work against Dialga (I think so) but her Incorporeality will make her resistant or even immune to most of Dialga's powers (Except if he has the ability to hit Incorporeal/Intangible beings)
Soul Manipulation: Well, Dialga probably don't have a Soul, so i think this will be useless against him
Time Manipulation and Reality Manipulation: I don't know how Chara uses Reality Manipulation, and Time Manipulation is probably due to her saves, and i doubt it will work on Dialga, since he is the embodiment of Time and rules over it, as well as the fact that he is Acausal too
Acausality: Like i said before, Chara's Acausality will make her immune to Dialga's Causality Manipulation and Time Manipulation, and it will make her pretty hard to kill, except if he uses Reality Warping to take care of that
Finally:
Well i don't have any idea of who is on the higher-end of Multiversal, and they are resistant/immune to each other's powers, and Dialga's only advantages are Reality Warping and possibly Spatial Manipulation, while Chara is immune to most of his powers too, and is Acausal and Incorporeal
So i think its Inconclusive or Chara wins