Cross-training - do gym work to build your core strength and endurance. Avoid bulking up though.
Technique - find hill climbing positions that work for you.
Lightness - drop all your water except a couple mouthfulls before the climb. Don't take anything up that doesn't directly contribute. No tools/pump/spares. Remove excess clothing too - you should already be warmed.
Timing - Ride with a tail wind up the hill on a cool morning.
Records - keep accurate records of your progress... strava segments are awesome for this.
Attitude - Think "I'm gonna do it - going to smash my PR! Going to go faster than Tim, better time than Harley!"
Motivation - follow someone faster than you up the hill, go into oxygen debt in the last couple hundred metres (ie flog it)
Bunch - Draughting on a climb is less effective but still useful. Ride the hill with a bunch if you can.
More motivation - join a race that goes up your hill.
Thank you for the strava link - heres some thoughts based on that.
Here's your time compared with the current KOM. I can't compare your run with your opponent.
I note that your efforts before crossing the A14 were not insignificant - doign a solid high 20km/h with peaks into the low 30s. Consider doing the first bit as a warmup ride, then dawdle from Swavesey to the A14 at about 10-15 km/h. Eat a gel and have a small drink on this stretch.
For the climb segment - you lost 8 seconds coming from the big roundabout, in the first 200 metres. Get up to speed before the start of the segment - that means start pushing up to speed as soon as you cross the A14.
The next 600 metres is pretty good - you're at about the same speed as the KOM holder through to the left-right wiggle before the two little ponds. This is good.
Finally, KOM holder just rolls away by maintaining a steadily-higher speed. Your only option here is to push harder and not allow any localised steep bits to slow your momentum.
The elevation graph shows a dip at 1100-1200 metres. Is that real or a map artefact? If it is a real downhill you should be pushing real hard from 1000 metres and be accellerating as you crest the brow. Then push down the downhill until you can't pedal that fast, at which point you should be all aero. This is your brief moment to rest. As the road rises again you start pedalling as soon as you can do so effectively. Then change through the gears to keep your cadence up while applying lots of power.
Keep applying power all the way through Boxworth. Once you pass the pub/in then get out of saddle and and you should be at full speed passing Battle Gate Road to follow into Elsworth Road. Sprint right through the ending then coast down and rest.
Your HRM data shows a max of 160 BPM, which is hard work but not near peak for your age. I'm 42 and still below average fitness, and on a hard-yakka climb will sit at 175 BPM spiking to 180 BPM when motivated.
Your overall ride data that day looks good - 1.79 W/kg is a solid effort.
Other things to help
Set your sights on a rider in front if possible, and work to catch them.
Music - Eye of the Tiger, Mortal Kombat, Bob the Builder, whatever does it for you.
Ride with other (fast) people for draughting / drafting effect.
Do the ride on a day when there's a decent wind from the north or north-east (not sure of your local winds, but for me a nor-wester or howling southerly is a great boost)
Do the ride early, when there are fewer cars about. Use more of the lane than you might otherwise if sharing the road nicely.
Clipless pedals, if you don't have them, can be a boost. Personally its mostly about being able to unweight the rising pedal and not loose the foot position, but for very short durations you can pull up on the back pedal for additional power. Good for getting over a short hump or around a switchback.
Lastly - target this segment only. This is a sprint over 2400 metres, its not the whole 28km ride. Put ALL your effort into this one stretch of road only. Strava says its 33 metres of elevation change - you don't need to pace yourself for this. Smash it!