I can certainly tell you what I did to get these badges—I don’t know if my way was the best or most efficient way to do it (and if anyone else has tips or tricks, please share! Let’s pool our knowledge!), but here’s what I did.
[Side note: I definitely didn’t go for these badges at the same time. I focused on island medals first, then diving, fishing, and bug catching. I suppose you could work on getting them all at the same time, but that seemed like way too much for me.]
Balloons: I didn’t do anything special for this—just popped every balloon I came across—but it might help to play the game for longer periods at a time (maybe half an hour or more), because that gives the game time to generate more balloons. When I got the gold badge for this, I was averaging 45 minutes per play time, so that might have affected the number of balloons I encountered.
Fishing: IMPORTANT THING TO KNOW—the fish you catch in Island tours, as well as on the Island generally, counts towards this badge. That also goes for diving fish and for bugs.
Whatever you do, getting this badge will be tedious. You need to catch 5,000 fish for the gold badge. By the time I decided to go for gold, I already had silver (which means I’d already caught 2,000 fish), so I knew I needed to catch 3,000 more to reach that goal. I figured the most manageable way to do that would be to give myself a month—if I caught at least 100 fish a night, I’d have the gold badge in a month.
So that’s what I did. I’d empty my pockets of everything but my fishing rod, go to the beach or river in my town (I often switched between them), and just catch every fish I saw until my pockets were full. Then I’d sell the fish at ReTail and start over. I kept a running count on my phone (every pocketful = 16 fish) so I could track my progress.
I did try fishing on the Island for awhile, but I didn’t find that to be any faster than fishing in my town. Sometimes it was a nice change of scenery, though.
Diving: Basically the exact same strategy as above, except you only need to catch 1,000 for the diving gold badge, so it’s way faster. Again, diving on the Island didn’t seem to be any faster—in fact, sometimes it seemed slower—than diving in my town.
Catching bugs: Okay, this one is SO MUCH EASIER ON THE ISLAND. Getting the gold badge for this was much faster than for fishing, though my strategy was basically the same. Again, I knew I needed to catch 3,000 bugs for the gold badge (I already had silver for this one too), so I knew if I caught at least 100 a day I’d be done in a month. But because catching bugs is so much faster than catching fish, I was usually able to catch 200-300 a day.
Visit the Island in the morning or the early afternoon, when the daytime bugs are out, because they’re less rare and skittish than the nighttime beetles and stags, which makes the whole process faster. Catch every bug you see on the screen (they’re usually hanging out on the middle earthen part), and when they’re gone, just walk around the beach until more appear. When your pockets get full, you can sell the bugs to Leila and then start again.
Island medals: This is another badge that’s just going to be tedious to get. You need to win 5,000 medals to get the gold badge, which means you just have to spam the hell out of island tours. The best one to spam is the Scavenger Hunt. It’s the shortest tour with the most reward—you get 16 medals if you finish with over a minute to spare. And honestly, you start to memorize the furniture really quickly, so the more you play the faster you are at it. Another good one to spam (if you can play with another person—it’s kind of hard with one person) is Item-Matching. It’s another short one, and you get 12 medals for finishing with over a minute to spare. Sometimes I’d spam the Bug Free-for-All if Scavenger Hunt wasn’t available, because even though it takes longer, you get 15 medals for getting gold.
But seriously, just spam the crap out of the Scavenger Hunt whenever it comes up. It’s an easy tour to play alone and it’s the fastest way to get the most medals.
Hope that helps! Getting these badges isn’t hard so much as it’s time-consuming. If you’re prepared to spend the time on it, you can definitely do it. Good luck!