The transition to 4* tier is definitely and unjustifiably broken and instead of having been solved, it has been made worse in the last few months. That said, it’s not impossible to inch forward and there’s good advice on the thread already.
The biggest source and greatest leap forward in the transition for a 3* player like you is the 40 Legendary Tokens that you got from championing. If you are anything like me, over half of them were worthless Invisible Women, Chulk and the such, but that still should have left you a sizeable number of decent to good 4s half-covered. Establish a goal now to focus your efforts in getting the covers for the good 4s you have with the most covers and the best 4*s (JG, HB, IM, Rulk) regardless of how many covers of them you have. You have limited resources, time and energy so it’s important to use it all where it will provide the best results.
1k progression in PVP is the main source. If it is difficult for you, don’t waste your efforts and HP in trying to get, say, a Star-Lord. But if a cover you really need is up there, spend as much as necessary of your resources and time to get it. Jump in a PVP bracket early (preferably with over a day to go) so you’ll have time to pay at your pace, recover health and packs, and use retaliations advantageously. Once you go over 600 points play until you get 800 or so, then shield and hop from there. It used to be that a 3* transitioner could shield-hop once and unaided from 800-ish to 1k, but latest changes have made their battles take much longer (and be more difficult) while climbing 4* players can snack on them in matters of seconds. Joining a Line truce or battlechat room is the best way to diminish the amount of people who would hit on you, while allowing you to get reliable targets that give high points (and if you’re lucky, cupcakes.) I’ll be the first to admit that is a bit of a hassle and an additional time and energy commitment to the already demanding MPQ, which is why I advice to only do it for covers you really want/need.
The second source is PVE. You can only be top 10 if you manage to play close to perfect (i.e. start at the very beginning of each sub, replay each node as close as possibly (and as quickly as possibly) to every 8 hours and grind the nodes to as low as humanly possible in the last 2 hours or so of a sub. This, I realise, is not possible to everybody, even with the different time slices. The ones that straddles your sleep time coincide with your job or family time, etc. It’s not for everybody, sadly (and even if it were, only the top 10 of them out of 1000 would get the rewards anyway). If you fall in that big group, PVE is still a venue for 4*s via the progression 25CP and the reward vault.
- Getting the CP progression reward is for everybody and can be done at your own pace as long as you play enough. A good rule of thumb is to play full point nodes at least thrice per 24h sub, but since latest subs give much more points than the earlier ones, you can slack quite a bit at the beginning. Find your own rhythm. Use the 25 CP to buy classic legendary tokens (never “latest”). Again, if you’re anything like me, you’ll get an unholy number of Invisible Women, but from time to time, you’ll get something good.
- PVE vaults are only 80 items big and have three 4* covers and one LT so every draw is a 1/20 chance of opening something good. IF the three 4*s are covers you need (or at least two of them are covers that you really, really need), is not a bad idea to try your luck buying covers. The single-draw daily deal is only 100 hp, so, coupled with the tokens you earn from playing the event, you can get around 10 draws total from the vault in the default 4-day event, which gives you a theoretical 50% chance of opening one of the big rewards.
The third source is the SHIELD simulator 2k reward. Play throughout the month, don’t leave it for the last couple of days. There’s not much else to say about it.
The fourth source is Crash of Titans in DDQ. You either can do it with the character as you have it, or cannot, but you’ll be surprised by how low you can sometimes go and still make it, don’t give up after a couple of times, unless it’s clear that is entirely useless to try.
Last, but not least, if you have a really good 4* with only 1 or 2 covers to finish, and you know that it will not come back again as PVP 1k reward for a while, it may be a good idea to save up the CP to buy them outright. It may be tempting to cash out 6 tokens instead, but if it’s a really good character, it will actually help you getting more covers more easily and reliably in the long run.