I never really thought about the Narada in battle until reading some of the above comments. In the finale of the we see the Enterprise phasers at the 27 Narada torpedoes and has no trouble destroying them. Given they were not targeted at the Enterprise but the Jellyfish. Also at the beginning of the film the Kelvin's phasers had no trouble shooting torpedoes down that were aimed at the shuttlecrafts escaping the fight.
With those being the facts. It seems surprising that 6 Starfleet ships were not able to damage the Narada with their weapons before the Enterprise arrived. With how long the Kelvin lasted against the Narada. You would expect these new ships; 25 years after the Kelvin attack would be able to last longer in a struggle. The same can be said about 47 Klingon war birds. Unless the Narada was shooting "one-hit total destruction torpedoes" against the Klingons and the Starfleet rescue fleet. It seems implausible for the Narada to survive those encounters against such odds. With how long it took the Narada to destroy/disable the Kelvin mind you.
Unless you use the "plot dictates" everything in the movie. Like max warp for the Enterprise from Earth to Vulcan taking 30 minutes to an hour in ST09 but 3 days for the refit ENT in TMP.