The proper rendering of Romans 8:4 is, "That the righteous requirement of the law might be fulfilled in us" (Rom 8:4 - NKJ). There was only one requirement of the Law covenant, which was the same for the covenant God had with Adam and Eve; obedience or death. “The soul that sinneth, it shall die” (Eze 18:4, 20). “And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat: But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die” (Gen 2:16, 17).
It does not say “the Law might fulfilled in us” but the “requirement of the Law might be fulfilled in us”. Before the requirement of the Law could be fulfilled in us, Christ had to first fulfill it in Himself; which He did when He said “It is finished” (John 19:30). Because Christ’s perfect life of obedience qualified Him for sacrifice, redemption was not procured through His obedience to the Law, but by Him being "obedient unto death, even the death of the cross” (Phil 2:8). "God sending His own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh" (Rom 8:3). This broke the curse of everlasting death - through the "Everlasting Covenant" (Heb 13:20).
How is the “requirement of the Law” fulfilled “in us”? The Father identified us with His Son in His death to sin; “How shall we that are dead to sin, live any longer therein? “Now if we be dead with Christ . . . .” “Likewise reckon ye also yourselves to be dead indeed unto sin.” “Wherefore if ye be dead with Christ . . . .” (Rom 6:2, 8, 11 Col 2:20).
For the Law to be effective (which was not its intent - Rom 8:3), one would have to obey it perfectly without ever breaking any part of it, which only Christ could do. "For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all" (Jam 2:10). To "redeem us from the curse of the law" Christ had to be "made a curse for us" (Gal 3:13).