If we wish to be like the Savior, to know what he knows, we must imitate his suffering. But it is important to notice that the word translated "suffering" in 1 Peter 5:10 is broader than the English term "suffering." It means "to experience" and "to endure" as well as "to suffer pain." The promise implicit in Peter's prayer is that if we endure the experience given by God, we will meet the requirements he has set for us, we will be made immoveable ("stablished"), strengthened, and set on a foundation stone ("settled"), presumably the foundation stone of Jesus Christ (cf. Eph. 2:20).

I take the Book of Mormon prophet Mormon to teach the same thing in different words and, at the same time, to give us a key to understanding how being perfected is possible:

Wherefore, my beloved brethren, pray unto the Father with all the energy of heart, that ye may be filled with this love, which he hath bestowed upon all who are true followers of his Son, Jesus Christ; that ye may become the sons of God; that when he shall appear we shall be like him, for we shall see him as he is; that we may have this hope; that we may be purified even as he is pure (Moroni 7:48).

If, as I suspect based on little more than intuition, Matthew 5:48 is an allusion to Leviticus 19:2—"Ye shall be holy: for I the Lord your God am holy"—then Moroni tells us how holiness, in other words purity, is achieved: I must pray to be filled with love; and to have that love is to truly follow, to be like, Jesus Christ. It is to become a child of God in the fullest sense. The gift of love is the result of prayer and it is through the gift of love that I become perfect, like the Son of God because loving like him.

Another Book of Mormon prophet, Alma the Elder, describes the goal of that Christly love when he addresses people who wish to be baptized:

Ye are desirous to come into the fold of God, and to be called his people, and are willing to bear one another's burdens, that they may be light; yea, and are willing to mourn with those that mourn; yea, and comfort those that stand in need of comfort, and to stand as witnesses of God at all times and in all things, and in all places that ye may be in, even until death (Mosiah 18:8-9).

This describes the perfection that Jesus demands: to be willing to bear one another's burdens without asking whether I deserve to or whether the person with the burden deserves it; to be willing to mourn, genuinely, with mourners and to comfort those who need comfort; and to endure to the end as a witness of God by living the life of love given to me.

On this understanding of becoming perfect, the question of to what degree I can become like Jesus in this life is moot. I must be fully what I am given to be through fervent prayer and, as Mormon's son Moroni later says, by denying myself all ungodliness (Moroni 10:32), which I take to be the same thing. I do not need to compare myself to others or to demand a yardstick for deciding how perfect I am. It is enough to submit and to love. In this life perfection, being like God, means being imbued with the love given by God, a love exemplified in the life of a Savior who willingly suffered unjustly, suffered that which he did not deserve, bearing our burdens, mourning with us, comforting us, and standing as a witness of the Father.