Now, what if he had done better at any of this?
First, we have to take in account that Hunnic hegemony wasn't an empire at the very least in the modern sense, and even as a "steppe empire" (too few nomads).
It's a personal construction, led by a charismatic leader, a mix of several different peoples (mainly German, then Iranian, and some Huns) and with an unstable aristocracy (without the presence of what is a Late Antiquity
imperium or what it implies, such as taxes and absence of fixed social roles) made in good part of Romans.
Some peoples were more or less submitted, but you simply didn't had an integration in a whole group : it's more comparable to what you have in Rhineland, political and military alliances between different cohesive peoples and tribes.
And, in fact, Attila's hegemon pretty well integrated such leagues under his domination.
It highlight what was said by others : Attila's strategy was quite sound there. It was essentially pragmaticst and based on tributes acquisition rather than establishing his domination on Romania proper, would it be only because military success and gain of wealth was the only way to keep his alliance to fall apart.
Hunnic hegemony simply lacked the infrastructure to launch a conquering campaign, and barbarian foederati (as well non-foederati established in Romania) were the main obstacle to a free ride in Italy (as they were in Gaul).
So while Gaul and Italy being entierly plundered is already hard to reach, taking over Constantinople is quite doomed from the start : the city was extremely well fortified, beneficied from a powerful navy to get supplies (when Attila didn't). Even Avars failed so while they beneficied from Byzzies being busy with Arabs, so...
I can see a Hunnic state surviving yet also not being an existential threat to the West.
Indeed, here's something I proposed a while ago, if it might be of interest.
For that it survives Attilla's death, giving a look at these leagues rather than Avars or Mongols is probably interesting.
That implies : military success and integration in romano-german geopolitics.
I would tend to think that killing Attila in 449 (IOTL, the assassination attempt failed) or slightly later would help : a less ambitious and "hunnic"-minded leader could better fit these.
Let's be clear, it would have relativly little macro-historical impact historically : I could see well a more limited Hunnic hegemony replacing Upper Danubian peoples (as Herulii, Lombardii, etc.) and heavily "germanized" (meaning heavily romanized as well).
Basically, germano-roman agglomeration of peoples, whom ethnogenesis would be based on their contact with Romania, and that would keep the ethnonym of "Huns" or maybe identify themselves as "Scythians", and establishing themselves in Romania either creating their kingdom in Romania (Italy or Illyricum, maybe Moesia or on its marches (as Gepids IOTL) along Danube.
Better in this case is relative, and if you play the scenario out you're just looking at OTL except the migrations would be replaced with raids
It's really hard to point Hunnic migrations there : not only Huns as as distinct people is made of several more or less indigenous groups (indigenous in the sense they lived there for centuries), but as for every other Barbarian groups, they scattered into different places even during Attila's reign. A Barbarian foedus isn't were an already distinct people came to live, but where a group lead by an aristocracy (defined by Rome) agglomerated different groups and created a people out of it.