Here are some questions I think will come up regarding negotiating with monsters.
Can't my PC use Intimidation to bolster Diplomacy?
Sure. Complementary Skills work normally. However, it's not just a flat roll against Intimidation. The penalties that apply to an Intimidation roll will affect this normally. If you still succeed, you get a +1. This does inevitably color negotiations to a degree - you might get the "my kind of scum" reaction but you might also inspire resentment.
Do we get a bonus to Diplomacy if we've killed a bunch of guys to make them respect us?
First, see Intimidation, above.
Next, you might get an unwilling negotiating partner to the table this way, but it will make negotiations tougher in most cases. Callous enemies might not care that you killed their friends, but if you whacked the dragon's mate and then try to negotiate on the "now you get twice as much treasure in this deal!" you're going to be in trouble.
Diplomacy isn't about relative power, ultimately, it's about deal making. A more powerful party might not need to offer as much, but that's resolved by roleplaying not by giving a bonus or penalty to Diplomacy.
How about bribes?
The better the deal you offer, the higher the bonus to your Diplomacy skill roll. Or it might obviate the need for a roll at all. A direct bribe is effectively a better deal offer and will get to the roll faster and may get a bonus. A poor deal that you insist on might not get to a roll, or it might be a roll with a penalty (hey, maybe they are desperate or you are persuasive.)
Hopefully that'll head off some at-the-table discussion so we can get right to the deal making and the die rolling.