As far as I know, the field promotion opportunities are:
- When you successfully storm the trenches in Toulon 3 times. Napoleon praises you to the government and you get promoted to Chef d'Escadron if your rank is lower.
- When you took the bridge in Arcole two days early by either waving the flag while marching alone or singing La Marseillaise. You get dined in Milan for a month and promoted to Chef de Brigade. Requires your MC to be an infantry officer.
- When you govern Treviso well in Italy, by burning Dumas's angry letter to Berthier and skipping the battle of Klausen. Napoleon will promote you straight to General of Brigade (if you are a Major) when you meet him in Toulon for the Egyptian expedition.
- Alternatively, if you successfully held Dego, Napoleon will offer you promotion up 1 rank to repay his favour. If you are a cavalry officer, you should save that favour for later (+ telling the truth about Josephine) if you want to save Dumas from Egypt.
- In Egypt, you can get a promotion up 1 rank by participating in the Syrian campaign. If you are a General of Brigade already, infantry MCs are automatically promoted to General of Division to replace Bon following his death. Cavalry MCs will have it a little harder since they have to compete with Murat for the promotion, but you can capture the Ottoman general with him and win the promotion without losing his friendship or turning him into a rival. Just shoot the Ottoman dude instead.
- If you are a General of Brigade at the end of the Egyptian campaign, upon your return to France, the Directory will promote you to General of Division if you have around 120 rep with them. Not exactly a "field" promotion but I'm not complaining!