How do you get badges for you heroes fast as a f2p player and how does p2w players upgrade all their heroes to maximum bagdes immediately after an increase in team level and badge level?
I find myself working on 1 hero for a long time with a very slow progress.
The answer, my friend, is stamina pots. Consumable items that each give 60 stamina when used. They’re given quite often in bundles, and there’s double drop items too. Even as a f2p, you might be able to snag a few if you’re lucky.
If you wanna get badges fast, stock up on energy till a 2x normal campaign drop rolls around. Once that happens, tyou will have endless raid credits and can get badges for as long as you have enrgy. Hope this helps 
As an example: I got three of my characters from P4 to O0 using this strategy 
Okay, yes I normally also buy the stamina deals when they pop up and also bagde deals when they are offered for diamonds. But still I feel like when I use for example 150, 60 energy items as well as a double drop item its not getting me a lot. Currently I have 15 heroes O2 and level 100 but at this point getting a badge requires a lot of energy and to get 15 heroes to O3 just feels impossible.
There is no real answer to that rather if you are fine with the pacing as you progress no matter how much it takes. In case you are fine not recieving much team lvl and wait for double drops, @Champion_David gave a good solution. The other one even tho haven’t seen it quite a while is wait for badge bundles, keep always a few extra diamonds. Last one is get stamina fills from bundles and contest.
Look out for a badge bundles for diamonds deal, they roll out a few of those every now and then if you’re a f2p player.
If you’re a p2p player you can buy a badge bundle deal, they’re quite common
Getting 15 heroes to O2 sounds impossible to me, so I feel you on this.
if your having trouble possibly pay money or around that stuff,
tell me if this works
As people have said, wait for double campaign drops and then use the extra stamina stuff and get 2x the badges. Doing team trials also helps give you many badges.