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he tried really hard

while fighting frieza with all his might, frieza was winning until goku used the spirit bomb. after that, even though frieza seemed to be destroyed he arised from the deapths and decided to kill everyone with a serious look in his eyes. so in order to torture goku he grabs krillin with his telekinetic or whatever that is power and makes him explode from the inside. goku then became furious and he totally snapped. since krillin was his best friend and he had once been revived by the dragonballs using them again was not an option. his fury turns into the sole purpose of beating the crap out of frieaza and begins to call upon every ounce of his remaining power and tries to forcefully produce even more. with his rage as a catalyst he draws enormous amounts of energy which gradually turn him into a super saiyan. no need to say that after he becomes a super saiyan, even in that beaten up state, he still beat up frieza so easily that he didn't even break a sweat.