Learn Russian: Если бы не этот свирепый зверь, мы бы не мчались так быстро. - If it were not for this fierce beast, we wouldn't be rushing so fast.

The construction если бы не (if it weren't for) is a fixed phrase that always takes the Nominative case. Even though не is present, it doesn't indicate the literal absence of the beast (in fact, the beast is there causing them to run!), so the Genitive of negation doesn't apply here.

How would we use the Metaphorical Instrumental from this lesson to say "we wouldn't be rushing like a fierce beast"?

You would put the noun phrase in the Instrumental case to describe the manner of the action: мы бы не мчались свирепым зверем. This structure is frequently used with verbs of motion or sound to creatively compare the subject to something else without needing the word как (like/as).

Could we omit the second бы since we already used it at the start of the sentence?

No, in Russian counterfactual conditionals (hypothetical or unreal situations), you generally need the particle бы in both the condition clause and the result clause. The first бы belongs to если, and the second creates the conditional mood for the verb мчались.

The verb мчались is imperfective. Since conditionals often use the perfective to show a definite result, why use imperfective here?

The imperfective is used because the action is an ongoing process. The speakers are currently in the middle of rushing. If you used a perfective verb, it would focus on the completion of the action or successfully reaching a destination, rather than the continuous speed they are experiencing right now.