Repentance: Strong's 3341, transliterated as "metanoia", and is literally a "change of mind", and is brought about by a condition of sorrow and abhorrence for past misdeeds or evil actions.
Young's Literal Translation of Luke 24:47 reads,
" and reformation and remission of sins to be proclaimed in his name to all the nations, beginning from Jerusalem:"
Reformation / repentance is a change of mind because of a recognition of the evil of sins. That change of mind, that recognition of sin that separates us from God, must come before we can be forgiven. It entails sorrowful intent, and a turning back to God, to walk with Him.
Those who continue in their sins have not yet had that change of mind. They have not yet made that final determination to stop. I am not sure what you mean by "complete/perfect" as that is not in the scripture, but if you are referring to an absolute repentance for a particular sin, that is an individual determination to stop sinning; and it needs a greater desire to love Christ, who sacrificed Himself for us, more than we love ourselves (Matt. 22:37).
" And having heard, they were pricked to the heart; they say also to Peter, and to the rest of the apostles, `What shall we do, men, brethren?'" (YLT)
The sorrow that causes us to be "pricked to the heart" will cause that change of mind.
"And the wicked -- when he turneth back From all his sins that he hath done, And he hath kept all My statutes, And hath done judgment and righteousness, He doth surely live, he doth not die.
22 All his transgressions that he hath done Are not remembered to him, In his righteousness that he hath done he liveth." (YLT)
"and `their sins and their lawlessness I will remember no more;'and where forgiveness of these [is], there is no more offering for sin." (YLT)
Christ's blood washes us clean once we have repented of our sins (Acts 22:16). The answer then is, "YES", repentance is necessary for forgiveness, and for salvation.
It is a process. We have to recognize that we are in sin, and that the sin will separate us from the Father (Isa. 59:2; Jer. 5:25). We have to be sorrowful, being pricked in the heart at the realization that our sin is why our Savior was nailed to the cross. Our sorrow causes a change in our minds to stop living as the world would have us live in selfish desires, and instead to earnestly want and need to turn back to Him.
Christ is the only way to the Father, as no one comes to the Father but by Him (John 14:6). Once we have repented, then we must be immersed in water (baptized - from the Greek baptizo, to dip fully or submerge) in order to come in contact with the blood of Christ (Acts 2:38, 22:16; Mark 16:16; Rom. 4:7, etc.).
We are baptized into Christ, putting Him on (Rom. 13:14; Gal. 3:27) and are covered by His blood, then we can ask God's forgiveness and receive remission of sins. Having come into contact with the blood of Christ, His blood covers us just as the blood of the lamb that was painted over the lintels of the doors in the last plague of Egypt, and in the same way the judgment passes over us... as long as we live for Him, and continue to be repentant when we fall and stumble. If we die in the Lord, faithful unto death, that judgment will pass over us!
But, if we stumble and turn back to the world, and turn back to sin, it will separate us once again from our heavenly Father.
"For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins,
27 But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries."
We cannot use the blood of Christ as a bargaining chip. God will know the intent of our heart, and those that premeditate the commission of a sin, and then try to come back and say, "Oh, I am sorry, please forgive me"... well, He will know that foreknowledge of the sin was in your heart. There is no repentance with foreknowledge, as that sin crucifies our Lord and Savior again.
" If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame."
"Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace?"
Repentance (change of mind), then forgiveness / remission of sins, and we are united with the Father through Christ to be restored to Him, to be counted worthy of life eternal (John 3:15; 10:28; 17:3; 2 Thess. 1:5)
"Who will render to every man according to his deeds:
7 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
8 But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath,
9 Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile;"
The promise is to all those who continue in His word, who continue to walk after Him, and to seek Him every day. It is not easy, and there is a cost by denying the approval of the world, and the the fellowship with the world which is enmity with God (James 4:4).
We fall, we repent, we pick ourselves back up and turn back to Him, and ask His forgiveness, and we have the promise of the remission of those sins. They will not separate us from our Father in heaven as long as we repent of them.
" For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come,
39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord."
Once covered by the blood of Christ, should we turn our back on Him and fail to repent, fail to keep trying, fail to seek Him, we will have lost that salvation. So, repentance is a continual process, because all of us fall short of the glory of God (Rom. 3:23).