For any gold challenge you need good teammates. If you are using the inbuilt match making system you usually end up with fairly bad players. You probably will never finish the gold challenge with random teammates unless you are incredibly good or come across some good randoms.
First follow the guide I wrote about carrying your team. You can find it here. I also suggest that you only try the gold challenge once you have ranked your class all the way because the power buffs are very important for the gold challenge. Also the more missiles and self revives etc you have the easier it makes the gold challenge. These come with buying upgrade packs.
Effective Classes Against the Geth
The Quarian infiltrator is very good against the Geth because they can Sabotage synthetic enemies to fight for them for some time. This is very useful against Geth Prime. A lot of Geth Prime spawn in on the gold challenge so making fighting them easier is key. Other than that, the quarian infiltrator isn’t that good a slayer unless you use a powerful sniper rifle like the Widow or Black Widow. As an infiltrator you can complete the 4 part objectives using your cloak. It will last the whole time the objectives take to complete. You can also easily revive downed teammates out of bad situations so that they don’t have to self revive.
The vanguard is very effective as a slayer against the Geth. The Geth don’t have troops that can instant kill you so don’t worry about being careful with who you charge. You can find a guide to level the vanguard effectively here. The only enemy you shouldn’t charge is the Geth Prime because the missiles he fires stagger you and usually mean that you die. Only charge into groups of enemies where you can stagger everyone with charge and nova. Once they are done walking backwards your charge will be ready again. Charge and Nova provide you with invincibility frames which allow you to be very aggressive (you can’t be damaged during the charge and nova animation). Always let the Vanguard be host because the vanguard suffers the most from a bad connection.
Any class that has overload, like the human engineer, is very good against the Geth. You can find a guide to using overload effectively here.
Geth Gold Challenge Combat Tactics
The Geth Flamers and the Hunters are the troops that will kill you the most often. They try to get close to you and then can kill you very quickly. Be sure to keep an eye out for them and kill them on sight as fast as possible. If they get close to the main body of your team use rocket launchers to get rid of them. Geth Prime are the second most annoying enemies the Geth have to offer. However, the quarian infiltrtor can take advantage of them by sabotaging them to fight for you for a while. This is very powerful if you find one at the start of a round because the Geth Prime will be bunched up with a lot of other troops which will probably include at least one more Geth Prime.
The vanguard should take care of the smaller groups of enemies to make sure the main body of the team doesn’t get flanked. However, it will be ver difficult for the vanguard to take on Geth Primes and larger groups of other enemies. Be sure to wait a while into a round before starting to charge around and killing everything.
The other two team members should be spamming overload and using their heavy pistols to kill enemies in the cool down time of overload. They can together take care of large groups of enemies easily because they can stun around 6 of them at a time. This is also useful against enemies with shields.