As po1102 already mentioned: Unless it's a tower/colo(also Raising) event; there's no real chance to rank for 8*s unless you spend money.
I can try to help you from the experiences I made throughout this game: Popularity can end up crazy to rank in, because there's no group ranking and the gaps aren't that large as if you're ranking in groups. This means, you actually have to play more frequently. BUT you'd need a Eu 6*+, so save your pures for that if you really want to rank in a popularity event. It's quiet possible to rank for a princess, like Po said, but it all depends if they're wanted or not.
Training... Is more about spiking nowadays since many people tend to spend money and spike their way through, but it's possible to rank for 7*s in training. But it's like Po1102 said. You'd need to be grinding the whole event and you'd also need a Event Unit higher than 5* rarity, otherwise there won't be any use to try it at all. Event Unit 4*s aren't really helping in training events.
Raising is nowadays all about a team full of Event Units. You can make a full team out of Event Units, but I'd advice you to do it like this: You either have a full team out of Event UNITS with proper monsters to defeat bosses OR you've a full team out of Event MONSTERS with proper Units to defeat bosses.
Even if you only manage to buy Event Unit 5*s, they're pretty much useful with the stack bonus they're giving. I'd rather buy a team full of Event Unit 5*s than Event Unit 6*s or 7*s, because they're usually very expensive. Most importantly: You need EVENT ALLIES to find bosses and snatch them to get MVP which grants you a large amount of Bonus Points, especially if you've Event Units/Monsters in your team. Also Event Units + Event Monsters do stack. A lot of burning if required to rank. TE is more valued than potions in Raising events.
About Panel... Well... Forget it. As long as the rewards are unwanted, there's no real chance to rank high enough without spending money, because it's a pay2win event. You need a Eu 6*+ at least and many event items to get a lot of bonus points. If the rewards are unwanted, there's a slim chance to rank for a 7*, but you'd definetely need to burn.
Gifting is a another thing, because some sometimes it's possible to free rank since we do have the group ranking, but many times it's a pay2win as panel, especially since you cannot trade event units. You'd need to spend moneys to get a Event Unit.
Also, Collosseum and Tower can be used for free 8*s if they ever make EU's tradeable again. Ea Dragonsbane as an example was 100 TE if you had a Eu 7*.
Po said all I could say to Dice.
Just keep hoarding until you see a 7* you really want and you know it's reachable.
I hope this was helpful.