You have to become very familiar with sufficient and necessary reasoning. You need to be automatic, quickly recognizing conditional reasoning and diagramming it reliably. You can't spend a minute trying to figure out the meaning of "unless" or "if and only if." It might seem like diagramming can take a long time, but it is very valuable if you can trust what you have written down. You won't have to return to the stimulus repeatedly.
Conditional reasoning is one of the most important concepts to learn, for logic games as well as logical reasoning. Keep doing your missing premise and missing conclusion drills. You should know the contrapositive of a given statement just by looking at it, and you should be able to connect multiple premises based on their common terms.
In short, sufficient and necessary reasoning must become second nature to you. It should be the first thing you think about in the morning and the last thing on your mind before bed.