This is my first guide, sorry if things don't look quite right.

This is a guide to get both the Alone ending achievement and said ending (If you beat this card game you get let out alone, at least that was my experience) as well as the achievement for beating Death's card game.

After you meet death for the first time, not long after they will give you a trial, the trial is this handheld video game. Make a save before you go into the game that way you can always quit out of the game and load up your save if something happens. You can't scroll backwards through the game, so if you mess things up you'll have to start over and every time you do it it gets harder to actually restart the game as the give up/end game button (whichever it is) gets larger and starts to move around the screen to cover the 'retry/restart' button (whichever it is). This means the more you mess up the more likely you are to accidentally click out of the game instead of clicking to try again. The game isn't meant to be winnable because that's just Death's deal, they're kind of a jerk.

There is a timer in the upper right hand however, it doesn't appear to matter how long it takes you to complete this, if you complete it you win. If you look near the top of the photo you'll also see where it tells you "NEXT:" it will provide you with a card number and suit. it will go from 2-10, jack-king, then ace for a suit, then it will move to the next suit starting at 2 again and going through the process until it's gone through all 4 suits then you click the last joker card (it starts with a joker already selected and ends on the other joker).
Every time I restarted my game the order and placement of the cards was the same so it appears to be the same grouping every time, as such hopefully this answer is the same for all of you.