JOEL - Yes and no. First the No.
Perfection means that we are complete in every way possible. It means we commit no sin, know everything there is to know, and are able to do anything that can be done. It means we have died; been resurrected; and have received exaltation. This of course can not all happen in this life.
It is interesting to note that Christ did not yet consider Himself perfect (or complete) until after His death and resurrection. In Luke He told His apostles, refering to His death:
"..and the third day I shall be perfected."(Luke 13:32)
In Mathew he said:
"Be ye therefore perfect, even as your Father which is in heaven is perfect." (Matthew 5:48)
Now compare this to what He told the Nephites after His resurrection:
"Therefore I would that ye should be perfect even as I, or your Father who is in heaven is perfect." (3 Nephi 12:48)
Elder Joseph Fielding Smith explained:
“Salvation does not come all at once; we are commanded to be perfect even as our Father in heaven is perfect. It will take us ages to accomplish this end, for there will be greater progress beyond the grave, and it will be there that the faithful will overcome all things, and receive all things, even the fulness of the Father’s glory." (Doctrines of Salvation, 3 vols., comp. Bruce R. McConkie, Salt Lake City: Deseret Book Co., 1954-56, 2:18)
So the answer is No. We cannot achieve absolute perfection in this life.

Now for the Yes.
Although we cannot reach the perfection of God while here on earth, there must be another type of perfection that we can achieve relative to this life, as is evident in the following scriptures:

"that ye may stand perfect and complete in all the will of God." (Col. 4:12)
"For the perfecting of the saints" (Eph 4:12)
"offend not in word, the same is a perfect man" (Jame 3:2)
"Make you perfect in every good work."(Heb. 13:21)
"attain to a perfect knowledge of him." (Jac. 4:12)
"your knowledge is perfect in that thing." (Alma 32:34)
"Moroni . . . man of a perfect understanding." (Alma 48:11)
"that thy fasting may be perfect" (D&C 59:13)

President Joseph F. Smith said:
“We do not look for absolute perfection in man. Mortal man is not capable of being absolutely perfect. Nevertheless, it is given to us to be as perfect in the sphere in which we are called to be and to act, as it is for the Father in heaven to be pure and righteous in the more exalted sphere in which he acts." (Gospel Doctrine, 5th ed., Salt Lake City, Deseret Book Co., 1939, p. 132; italics added.)
Achieving perfection relative to our mortal sphere would probably include things such as; repenting of all our sins; walking by faith; receiving all the ordinances; being faithful to covenants we make with God; obeying all the commandments; seeking first the kingdom of God; and having unconditional love and charity to all mankind.
Obtaining all these things can't happen all at once.
President Kimball said perfection is a "process to be pursued throughout one's lifetime" (Kimball, Spencer W. "Hold Fast to the Iron Rod." Ensign 8 (Nov. 1978):4-6)
And of course we will never be aware of when we have actually achieved it; for the moment we feel we have reached perfection, we will have lost it to pride and lack of humility. Perhaps for us in this life time we should think of perfection as a journey rather than a destination. Become as perfect as we can in single things along the way and over time they will eventually add up to a more complete and more perfect individual.
A good talk on this subject was given by Russell M. Nelson called “Perfection Pending", in the November 1995 Ensign, page 86.