Let's start from the obvious things:
- When you bring the enemy pet below 50% health, your dragon indeed gets a 50% damage boost for one round.
- It's triggered on the backrow pets aswell. I don't know if the current movesets allow to do this but you can make use of it taking a wounded pet into the backrow and then performing an AoE attack.
- This racial puts dragons in specific relationships with flyers and beasts. The first ones can suffer badly because of that.
- From some reasons, if the enemy is still alive for several rounds, this racial triggers itself every second time as long as your dragon attacks and enemy's HP stay below 50%, so not only in the 1st round after the climax, but the 3rd and 5th aswell.
- This also causes a "bug" in the opposite way -- if you bring two enemies below 50% HP twice a row (e.g. Mana Surge killing two pets in two rounds), the second round doesn't grant you a bonus.
- If your dragon dies while it has already had a racial bonus, and kept attacking, the buff will persist no matter whether the racial was up this round or was due at another one.