I'm only shooting for neighbors that I like. So Avery, Cranston, Ankha, and Mac are the only one's I'm going for at the moment. I think I'm close though! I'm sending letters and presents attatched every other day! I'm even accepting rediculous trade offers. I don't really mind if I give away rare fish/bugs because I can always make up for the loss of bells at some point of the day.
I've also got Chief's pic. Also, if you stay in your house for a long time, those who've given you their pic will come over randomly and give you furniture. Chief gave me a throne.
Also, I din't send a ton of letters or anything. I just talked to them tons, gave them some favorite items and agreed to a bunch of requests.