Although I & II Peter claim the same author, they have large differences in style and approach. Second Peter is unrefined in writing style, more shrill and less gentle than the first letter. (Many scholars question whether the apostle Peter atually wrote the whole letter, but the first letter claims his authorship and shows some signs of his influence.)
Perhaps the difference in audiences explains the two approaches. The Bible views suffering - persecution from outside - as a purifying influence that often result in an even stronger church. Thus I Peter has an encouraging and devotional tone. But the real danger to a church comes from the inside from immoral behavior and false teaching. Second Peter, in strong words, addresses those "inside" dangers.
As you read it, try to put yourself in the place of the original audience. What dangers does the author warn against? Are there parallels today? Chapters 1 and 3 can be universally applied. Chapter 2 concerns itself more directly with the particular false teachers plaguing the first-century church.
In tone and actual content, II Peter resembles the tiny book of Jude. Both deal with the same problems and propose the same solutions.
When reading II Peter, look for the word knowledge, and related words like thinking, reminder/remind, and remember. The author appeals to true knowledge that can correct many of the young church's errors.