If Embessa goes to the battlefield, does her when I attack trigger resolve before the "shield" effect from my units? Can I play a reaction speed card to increase the might of my unit to prevent it from dying?

Yes to both — but the details matter.

1. Ambessa's attack trigger does NOT resolve before Shield's passive bonus. Shield is a static/passive ability — "While I am a defender, I have +X [M]" (Rule 814.1.c). It's active the moment your unit gains the Defender designation, which happens before any triggers resolve. The defending unit already has its Shield Might when Ambessa chooses her target and when her trigger resolves.

2. Yes, you can play a Reaction to increase your unit's Might and save it. While Ambessa's trigger is on the chain, the state is Closed and you can play Reaction-speed cards. If you boost your unit's Might so it's no longer "less than" Ambessa's Might, the unit becomes an illegal target. On resolution, the kill instruction targeting that unit is ignored (Rule 359.3.e.5).

Just keep in mind that Ambessa, Respected and Feared needs to be Empowered for the attack trigger to exist at all — and when she is, her Assault 2 also kicks in while attacking, putting her at 7 Might (base 5 + 2). So you'd need to boost your defending unit to 7 or more to dodge the kill.