Read more about Perfection from the works of the Mother and Sri Aurobindo.
What is Perfection?
Perfection is all that we want to become in our highest aspiration  ...man as a being is capable of self-development and of some approach at least to an ideal standard of perfection which his mind is able to conceive…  The characteristic law of Spirit is self-existent perfection and immutable infinity. It possesses always and in its own right the immortality which is the aim of Life and the perfection which is the goal of Mind. As you pursue this labour of purification and unification, you must at the same time take great care to perfect the external and instrumental part of your being. When the higher truth manifests, it must find in you a mind that is supple and rich enough to be able to give the idea that seeks to express itself a form of thought which preserves its force and clarity. 
One can attain perfection in the different parts of the being - in the mind, the vital and the physical.
Perfection of the Mind - Our mind, in its search for what must be, turns towards a concentration on our own inner spiritual growth and perfection, on our own individual being and inner living; or it turns towards a concentration on an individual development of our surface nature, on the perfection of our thought and outer dynamic or practical action on the world, on some idealism of our personal relation with the world around us; or it turns rather towards a concentration on the outer world itself, on making it better, more suited to our ideas and temperament or to our conception of what should be. 
Perfection of the Vital - Many of the things we need for our perfection, courage, will-power effective in life, all the elements of what we now call force of character and force of personality, depend very largely for their completest strength and spring of energetic action on the fullness of the psychic prana.  Perfection in the Physical - Perfection in the physical means that the body becomes conscious, is filled with consciousness and that as this is the Truth consciousness all its actions, functionings etc. become by the power of the consciousness within it harmonious, luminous, right and true—without ignorance or disorder. 
Why do we Need Perfection?
There can be no real perfection for us except by our inner self and truth of spiritual existence taking up all truth of the instrumental existence into itself and giving to it oneness, integration, harmony. As our only real freedom is the discovery and disengagement of the spiritual Reality within us. 
Mind, life, body, all the forms of our nature are the means of this growth, but they find their last perfection only by opening out to something beyond them, first, because they are not the whole of what man is, secondly, because that other something which he is, is the key of his completeness and brings a light which discovers to him the whole high and large reality of his being. 
So long as one remains in the world-existence, this perfection must radiate out from him,—for that is the necessity of his oneness with the universe and its beings. 
How to Achieve Perfection
We do not become perfect, but only shift the field of our imperfection or at most attain a limited altitude.  For this shifting of imperfection to perfection, the first step is to become conscious of yourself, of the different parts of one’s being and their respective activities. For becoming conscious of oneself, one must be quite awake, in a state of observation of one’s thoughts and actions; becoming clearly aware of these movements, noticing their reaction, impulses etc. With a constant observation and practice, one does not only become a witness of what is happening within them but will also be aware of the origin of these movements.
By silencing the mind and living in calm state is a step on the path of perfection. Those who have thus possessed the Calm within can perceive always welling out from its silence the perennial supply of the energies that work in the universe. It is not, therefore, the truth of the Silence to say that it is in its nature a rejection of the cosmic activity.  The calm established in the whole being must remain the same whatever happens, in health and disease, in pleasure and in pain, even in the strongest physical pain, in good fortune and misfortune, our own or that of those we love, in success and failure, honour and insult, praise and blame, justice done to us or injustice, everything that ordinarily affects the mind. 
Another important aspect is Faith. There is one kind of faith demanded as indispensable by the integral Yoga and that may be described as faith in God and the Shakti, faith in the presence and power of the Divine in us and the world, a faith that all in the world is the working of one divine Shakti. 
Mind, Body, Life and Integral Perfection
Our mind is partial, biased and always in search of what must be. It can turn towards the outer world and watch the world for what should be or turn inwards & concentrate on our own spiritual growth and perfection.
The obstacle to mind’s endeavor to perfection is its limitation to go beyond itself . The mind finds fully its force and action only when it casts itself upon life energy and accepts equally its possibilities and its resistances as the means of a greater self-perfection .
On the other hand, our body is a remarkable instrument - the most difficult to transform yet the most capable. Sleep, dream, exercise, illness, posture, beauty in movements are a few aspects of the physical culture through which perfection in the body can be brought. The physical body is a basis of action, pratiṣṭhā, which cannot be despised, neglected or excluded from the evolution: a perfection of the body as the outer instrument of a complete divine living on earth will be necessarily a part of integral perfection. When the body has learned the art of constantly progressing towards an increasing perfection, we shall be well on the way to overcome the inevitability of death.
Mind, Life and Body
Mind, life, body, all the forms of our nature are the means for the growth of the spirit. They find their last perfection only by opening out to something beyond them. The ego generally governs the development of the individual; however, as the individuality perfects itself, the power of the ego diminishes, the true individuality emerges, the individual upons to the force descending from above and thus moves towards perfection.
Yoga of Integral Perfection
A Yoga of integral perfection regards man as a divine spiritual being involved in mind, life and body; it aims therefore at a liberation and a perfection of his divine nature. It seeks to make an inner living in the perfectly developed spiritual being his constant intrinsic living and the spiritualised action of mind, life and body only its outward human expression.
Practical Tips to Perfection
One can perfect oneself for evermore, as Divine is the perfection towards which we move. It is our confidence and sincerity to transform personal imperfection which would help one become more and more perfect in the thoughts and actions. Our patience with ourselves to self-awareness and observation is key to this transformation. Inner and outer perfection is in the process of natural evolution, however, the personal perseverance of each individual would help to transform to greater perfection consciously.
Read more about Perfection from the works of the Mother and Sri Aurobindo.