Starlit Adventures

There is no easy way to do this. My advice would be:

Grind as many tokens as you can so you can keep on respawning if you die.

The costumes I had equipped were Arrow, Bomb and flying.

Eventually you'll see that levels start repeating so it'll be easier to navigate as you'll learn the patterns for each floor.

Keep track of how many chests you unlock.

As of right now, you have to unlock all chests in 1 playthrough of infinite mode (you can die and respawn as many times as you want, as long as you have tokens to do so)

A couple of notes from Seamus McLimey "Respawn cost caps at 8 tokens. And if your controller disconnects or turns off while you are in the game, you will automatically be sent back to the title screen. So if you don't have a plug in kit, make sure you have full battery life before trying this."

This is not cumulative across multiple playthroughs, all 50 chests must be opened in the same run.
I chose Arrow, Bomb and Snow suits and the achievement popped on Adventure Day 9, at 2785 feet.
I got the in-game achievement notification for opening 50 chests, then the actual achievement popped a few seconds later.

You don't need to collect gems so take your time and just focus on getting down safely.
Don't put yourself at risk to get heavily guarded keys, save your coins for the odd mishap and keep going for the next one.

I was a bit sloppy, I didn't get every chest and I used a lot more restarts than I should have, so it cost me around 280 coins.

A very useful advice.

If you run out of tiles and still don't get all the chests, use the cloud save cheat to get all the tiles back and try the tower again.

It also serves for the achievement of having the album complete.