I managed to finish Day of the Blade- Tough without issue, but I'm pretty sure it was only due to having a high level team so I can't really offer any suggestions to help people having a rough time.
Having issues running Gauntlet without getting wiped. Wasn't there some trick using low levels in your teams? I'd like to get a guaranteed reward by finishing it, but thus far I only managed to do so twice.
elty gave some good advice, but I'll try to expand on that a bit. As far as I've seen no one has done any real research into how the opposing gauntlet teams are chosen, only that team level has something to do with it and you can lower it by taking low level characters. I don't think anyone has experimented to see if character rarity or player rank are factors as well and I'm personally not willing to give up my gauntlet goodies to do the amount of testing that would require.
Team Composition
The general consensus is that you'll want at least 1 strong AOE character. For most people this will be Coro, but any AOE character with high damage should be viable. Next if you have Juliana or Phoena available you'll want one (or both if your team cost permits) in your sub party. You'll want to be able to 1 shot most opposing characters with your AOE and the sub party buffers are often critical to pushing your attack high enough to do that.
Here's where people tend to have different opinions and we really need more research to determine the best strategy. You can run your remaining slots as 1* LV1 characters which should substantially drop the rank of the opponents you fight or run ~4 other strong characters and fill the remaining with 1* LV1s. Either way I'd advise running a mono color team (ignoring sub buffers) so you'll always have the right color mana for the AOE skill. Option 1 means generally easier opponents and abundant mana from character deaths. The downside is you can't take much advantage of the sub healing glitch because all your fodder will be dead before long (preventing you from placing in sub), and any enemies you can't 1 shot will probably hurt your AOE character (possibly badly. Note that Coro's spin has a small window where she's vulnerable when the skill ends before you can use it again). This option also has an issue with buffers since you'll be sacrificing characters meaning your buffers will reinforce and muck up your mana.
Option 2 means harder opponents, but with a strong AOE character + buffer you should still be able to 1 shot most enemies. If you can't, you've got strong characters who should be able to finish the enemy off with a single hit. Since you have multiple characters who don't crumple instantly this is less damage focused on your AOE character. Plus you can utilize the healing glitch by putting characters into sub to fully heal them. The downside is you're more likely to encounter dangerous characters with AOE abilities that can instantly wreck you and you've got less mana generation from character deaths.
Formation
As elty alluded to, using proper formations can give you an advantage. Your character in the 1st slot will be in the center row. If using Coro or another non full screen AOE character you generally want them here so a single AOE can hit the full enemy front line. The character in slot 2 goes on the top row, slot 3 bottom row, and slot 4 center back row. This means if your opponent has 2 front row characters (warriors/knights) you can place a character in slot 3 so they don't have to push through the front line fighters and can walk straight to the back line.
If you've got LV1 characters you want to sacrifice for mana I'd suggest putting them in slot 2 or 3 so they run straight into one of the enemy's front line fighters. This will net you 1 mana right off the bat, so even if you start the battle with no mana carried over and only roll 1 on the roulette, you can still use Coro's skill almost immediately.
Selecting opponents
Sometimes you'll hit forks where you can choose between 2 opponents. Generally you should pick the weaker one, following the guidelines I'm about to give (unless you're at the last fork and you really want that prysma). When given the option choose teams that don't have an archer or mage. They'll probably hit you a few times before you get in range and there's a good chance they'll use their skill before you can reach them. Definitely avoid anyone with full screen AOE (Cheery, Aludra, Phoena).
If possible, choose a team that has 3 warriors/knights and a healer or dancer (an exception to the avoid ranged rule). You can kill the front line with one Coro skill, intercept the reinforcements (depending might want to use someone other than your AOE character since I've too often caught a healer with Coro's spin). At this point stall until you have 5 mana. With a dancer just move your characters out of the way of attacks until it starts dancing. With a healer it'l generally come up to hit you so I generally click and drag to swap character positions continually so I don't kill it too quickly. Starting a battle with 5 mana can make even the most difficult fights trivial.
A full warrior/knight party is easy pickings, but likely won't give you time to build up mana.
Combat!!!
Time to fight! Open with an AOE to take down the front row. If fighting a melee party, wait for them to come to you. Gives more time for the mana slots to pop up. If there's a dangerous ranged enemy, but full front line I suggest tapping Auto battle on then off so all your characters move up. An extra second of travel time can be the difference between victory and failure. Then move someone in to kill the ranged character (Coro will probably still be in spin animation at this point so she's not the best choice).
If you kill 2 characters simultaneously (which you should be doing with AOE) the reinforcements with come in stacked on top of each other. They'll walk up to their front line, then move to their proper positions based on class. You can easily get them both with an AOE while they're stacked.
Remember that your characters are invulnerable during their specials while opponents aren't. If things get bad, you can use a skill to save that character from a full screen AOE or other danger. Since enemies aren't invulnerable you can sometimes kill them before the skill goes off. Lindsey and other characters with quick activating skills are useful here. If you can kill the full screen AOE characters before their skill finishes (even if the meteor animation has already started) it won't deal damage if they die first.
Cheat
The enemies can use their skills without regard to cost or mana type so why should you play fair? Here are some notable glitches you can use to help.
Sub healing- Any character placed in your sub party will come out fully healed. If you're using high level characters you can put a different person into sub after every battle and rotate them around so you've always got someone to take hits.
Force close- If you close the app before you get the notification screen that you've lost (cuz all your guys died) you can open it back up with everyone just as they were before you entered the fight. Useful if you screw up, but it may not be enough if you're facing a strong team.
I use the team outlined in Option 2 and it's been quite a while since I failed to reach the last fork (where I consider the best goodies to be) and generally make it all the way through 74% of the time.