This trophy requires you to get 100 Gold Medal across both cop and racer factions. Here are a few hints. Note there are 68 medals in each career for a total of 136 medals overall. This means you don't need to gold every single event and can skip some of the tougher ones. I got to 62/68 in the cop career without much difficulty but the last few Hard hot pursuits were pretty nasty. Similarly in the racer career some of the Hard hot pursuits and races can be infuriating too.
Also, note that human players can potentially get involved while you're attempting these events so generally try and steer clear of them. The AI can sometimes get nasty but a good human player is a lot more dangerous. If it's really annoying you, just switch to a private game.
Interceptor: All straightforward to get gold on with any of the top-level cars. I used the Hennessy Venom [ENF] for most but got a few earlier on with the Lamborghini Aventador without much trouble. Choose EMP Level 4 and ESF Level 4, hit them as early as possible with the EMP, then the ESF, repeat, and you should be done in under a minute in most cases.
Rapid Response: These are mostly fairly straightforward with the Hennessy (or another decently quick car) although some of the harder ones take a little practice. Avoid hitting the walls at all costs - every contact is a cumulative half second penalty and these start to add up fast (0.5s the first time, 1.0s the second etc etc). A full-on crash ironically won't get you a penalty but obviously costs you a decent bit of time. You should be able to finish most despite one crash or a couple of bumps. Most are pretty do-able first time around, although some of the Hard ones will take a bit of practice.
Hot Pursuit: Straightforward at Easy and Medium, although the Hard ones range from fairly straightforward, to very difficult. There were around 5 or 6 that I found very hard because you basically just run out of road before everyone's busted. Generally either an ESF/EMP combo or an ESF/Spike Strip combo will do the trick. The spike strip can be effective if you can get out in front - placed at chokepoints you can get a hit on most/all racers with each use. Use gas stations to repair your car and replenish your tech during the race.
Interceptor: Generally very straightforward as long as you have the right car for the difficulty level. Wait for the cop to get close, use Shockwave (ideally fully upgraded), then pull a quick 180 and turbo away. Even the Hard interceptors can be dealt with pretty easily using this strategy. There were very few, if any, that I had to have a second attempt at.
Race: Generally the Easy ones are fairly straightforward, and the Medium ones mostly aren't too bad although the Hard ones can get tricky as both cops and AI use of tech can cause some headaches. Note also that the opponents will scale somewhat to your car level, so it's actually often best to tackle Easy and Med races with lower level cars.
Time Trial: With a fully upgraded top level car (I used the Ferrari Enzo Ferrari) these are generally all pretty do-able. Some of the Hard ones will take a bit of practice, but sensible use of Nitrous and Turbo, and avoiding crashes will make most of these simple medals. Generally easier than the Rapid Responses that cops get in place of these.
Hot Pursuit: The Hard ones can get pretty hard. Easy and Medium shouldn't give you too much trouble (note again that AI opponents seem to autoscale), but Hard can be pretty exacting, mostly from a survival perspective. In general, avoid using pursuit tech and ramming opponents (and cops) unless you need to because it'll keep your heat down and keep the cops a bit more quiet. Use repair stations any time you see one because the damage can rack up extremely fast if you're not careful.