To finish the museum collection, go fishing for the following fish first: Sea Bass, Bluegill, Crawfish, Frog, Crucian Carp, Catfish and other fish sold below 1,000 Bells. Give them to the museum. Now look for more expensive fish and donate them. Note: Donated fish will also become more common, so look into donating Snappers.
To finish the bug collection, first donate all four Cicadas, a Mosquito, a Fly, and a Honeybee. Also donate any common butterflies. Next, find the Stag Beetles (found at night) and the Oak Silk Moth. Oak Silk Moths are brown and hang on trees. Next, start digging up fossils. If it’s not a torso, skull, or tail, donate it. After you donate some small fossils like ammonites and dinosaur tracks, look for skulls. Donate Sabertooth and Mammoth skulls first since they are very easy to complete.
Also, save up about 5,000 Bells for when Redd appears. If you get Lyle and say which day you want Redd to appear, Redd will appear on that day. Buy a painting from him. If it is fake, dump it and fish for Snakeheads and Bass. If it is real, donate it. To also make the museum successful, go to the coffee shop once every day and after your cup, go back in the chair and say to Brewster, "I love this place!" if the option is available.