You go back to the start if you die, but platforming levels and the boss fights are completely separate. The longest fights in the game maybe clock in ~2 minutes, save for a gimmick boss in the final world.
You can get back into another run very fast in Cuphead.
Cuphead is hard, yes, but the boss patterns are pretty easy to learn. I highly recommend picking up the green homing shot and visiting the first Mausoleum ASAP, those will help make some of the bosses a little easier. I didn't bother picking up the extra hit point yet. XD
Can't really lose progress. It's just boss fights with the occasional platformer stage. 3 hitpoints at the start - you can buy more at the expense of damage output. Lose all your health, start the boss fight/stage over (or pause-retry as soon as you take damage >.>) I assume co-op is the same.
I saw a stream earlier tonight. Basically, you have multiple lives and infinite retries. You lose all your lives, you have to restart at the checkpoint. (There are a few checkpoints per level)
Wild Guns Reloaded is good for single-player for sure. You get infinite continues and can choose from 3 difficulties. Multiplayer, though, completely dropped the ball from the SNES game, aside from up to 4 players. Multiplayer has the difficulty decided by the number of players... (1/2)