Just to throw another option out there, this is pretty straightforward with index(match()) also.
Presuming you have the data like this (and adjust as necessary if you don't, including across different sheets):
Your max points column (k) would be:
=IF(MAX(INDEX($C$2:$C$4,MATCH(I2,$A$2:$A$4,0)),INDEX($G$2:$G$4,MATCH(I2,$E$2:$E$4,0)))=INDEX($C$2:$C$4,MATCH(I2,$A$2:$A$4,0)),INDEX($C$2:$C$4,MATCH(I2,$A$2:$A$4,0)),INDEX($G$2:$G$4,MATCH(I2,$E$2:$E$4,0)))
Your max achievements column (j) would be:
=IF(MAX(INDEX($C$2:$C$4,MATCH(I2,$A$2:$A$4,0)),INDEX($G$2:$G$4,MATCH(I2,$E$2:$E$4,0)))=INDEX($C$2:$C$4,MATCH(I2,$A$2:$A$4,0)),INDEX($B$2:$B$4,MATCH(I2,$A$2:$A$4,0)),INDEX($F$2:$F$4,MATCH(I2,$E$2:$E$4,0)))