Simple. Pray you go second. Draft fucking 2 drops and Class specific Evolution 4 drops. Draft good cards. By good cards I mean cards that are annoying to deal with and/or can trade 2 for 1. In online TCGs the random draft arena mode is ALWAYS about value and who is getting more out of their cards. Yes you still run into the blue moon constructed aggro, but largely arena is just about trading up and making your opponent expend resources and make suboptimal trades.

Also watch your curve and you deck composition. A card's value to your deck is increased or decreased based on what you drafted. Only have two 2 drops at 18 cards in the draft? That 2 drop now has a shitload of value. Have a lot of Necromancy cards? Burial grounds just got really good and Spirit Cycle goes from crapmundo to decent.

Its the same way for negatives. I stress 2 drops, but you don't need 15 of them. Cheap removal is good, but its woefully inefficient in the late game half the time so gotta be careful not to draft too many.

The only card you can draft an endless amount of is Beastcall Aria.