How would these effects resolve in Magic The Gathering?

Yesterday I was playing magic with a friend and he had a creature with 13/13 and another creature that when you tapped 2 Plains, it can make target creature indestructible. He then declared an attack with his 13/13 creature. I blocked creature with 2 5/5 creatures, lowering his toughness down to 3, after the battle phase had finished, during his endphase I hit his creature with a lightning bolt to take out the last 3 toughness his creature had. He tried to activate his other creatures ability to make his monster indestructible. My question is, would my Instant Lightning Bolt resolve first, destroying his 13/3, or would his other creatures effect make it indestructible even after I casted lightning bolt. The Damage is instant right? So immediately his creature was at 0 toughness and therefore dies, am I right?