Getting past those pesky arena missions
This is going to sound obvious and stupid, but it will help this click for you. There are only two ways you can win an arena match. Either you go first and kill the entire team before they go. Or you go second and you have a super defensive team that can just poke at the other team and out-survive them. In the early-mid game where you're likely stuck on the arena missions, it's going to be very hard to get a defensive team unless you were super lucky in shard draws.
This means you're going to need to use High Khatun, and 3 nukers. Something easily attainable is High Khatun, Spirithost, Warmaiden, Kael. Now the first step is to boost High Khatun's speed as much as you can. You're going to want all 6 pieces from the speed set. All 6 pieces should give speed. Your boots definitely need to be 5-star and +16. I'm at about 220 speed right now, and I can only out-speed about 1/3 of the teams. If you can get 230-235 that's great. If you 6-star and fully ascend her, she'll get more speed, so that makes it even better. Next, you need to adjust the speed on all your champs, so that khatun goes first, then spirithost, then warmaiden, then kael. Basically you want to make it so you can do the maximum amount of damage to try to kill the other team before they go. You'll still want to be at at least 160 speed on your slowest guy. The higher the better.
Now there's two keys to success. You have to go first, and you have to avoid unkillable champs. Avoid everyone in this picture. Most likely you will only be able to beat 1-2 opponents per reset. But by doing this you will climb. I've currently got 90 silver trophies, and I've been playing this game for 65 days.
The last thing you should be checking is level and Attack Power. I'm sitting at 80k Attack Power, and I'm able to kill teams at around 105k attack power. Above that and the gear difference becomes too high. There are teams that have 50k Attack Power and beat me, because they are faster. Attack Power isn't really a huge factor.