Lugia

To take a break from my training regime (for the purposes of levelling my team to battle Red), I decided to go and catch Lugia. I found a walkthrough on Youtube for finding Lugia's cave which proved to be really helpful.
As for catching  Lugia itself, it was a reasonable challenge. I used my level 74 Ampharos to weaken it. I let fly with a Discharge, thinking that Lugia, being a legendary, would have a relatively high Sp. Def. The attack caused enough damage to bring Lugia's HP to just below halfway. Then I followed up with 2 Strength attacks. When Lugia used Punishment, it got Paralysed. In theory, a non-volatile status condition would make the affected Pokemon easier to capture. In any case, I managed to get Lugia's HP down to a tiny sliver.
At this point, I stopped attacking and started throwing the Dusk Balls. I chose Dusk Balls for catching Lugia because I was going to be in a cave environment and Dusk Balls are supposed to be quite good for such environment as well as for nighttime battles. I had about 60 Dusk Balls in my bag, in anticipation of a long battle. After half a dozen Dusk Balls, I managed to get Lugia.
If only catching Entei was this easy...