Per HoH:TL, the only Hermetic Breakthrough was the Parma Magica.
In HoH:MC, the Mystery Verditius Elder Runes do not cover every Technique & Form, and each missing one could be added as a Minor Breakthrough. Deus Irae has a rather important breakthrough in it. (no spoilers, please).
Rival Magic, Hedge Magic, and Ancient Magic are filled with possible breakthroughs.
This thread is only for canonical breakthroughs already made. Since Bonisagus, what has been done that has improved/augmented/expanded existing Hermetic Magic?
Potential breakthrough projects is something for a different thread.
I haven't read Deus Irae, so I don't know what is in there, but I am now curious.
This is the sort of information that I am looking for:
What about Enchantment of the Scrying Pool, Whispering Winds and Wizard's Communion? They all speak of not being an entirely comfortable fit within Hermetic magic - would they have come about as the result of a Breakthrough?
Back in Bonisagus' time, spontaneous magic was something that Diedne helped with. Interestingly, Rival Magic suggests Viea stole the notes dealing with the limit of Energy and fatigue, so Bonisagus never did get to work on integrating this sort of magic.
It's not cannon but I'm not the only one to float the idea there has been a recent improvement in hermetic longevity rituals. This allows us to use the rules as is without populating our order with to many 300 year old magi. (this sort of mirrors the fact that in earlier editions the longevity ritual was not as effective)
There is a separate system to discover new mysteries (experimental scripts on page 18 of Mysteries Revised), it isn't the same as crating a hermetic breakthrough. I don't see why it couldn't be used to discover an initiation for a previously unknown virtue. (It often shouldn't as the virtue has to hit that sweet spot of both appropriate for the cult lore and not leading to min-maxy over specialization, but I don't see why it couldn't)
Aegis of the Hearth was a Major Breakthrough, per True Lineages p.27. It's an adaptation of both Parma Magica and a (previously non-existent) universal [Realm] Ward type spell.
It's also noted in Ancient Magic that incorporating a new extended duration (19-year) for Aegis of the Hearth would require an additional Major breakthrough on top of discovering the 19-year duration. This is likely due to the 'special' status of Aegis and other similar 'not fully integrated' spells.
Twilight was a Major breakthrough, and Certamen was a minor one.
Twilight Warping is by FAR the best warping of the organized groups, at minimum because those suffering from Twilight are nigh invincible. Also, it might be immortality.
The fact that the Form Arts provide Magic Resistance AND resistance to Form based effects (Terrem vs regular swords for example), was also a Major Breakthrough, and probably (?) lead to the development of Parma Magica.