There are a total of 8 caverns that you need to get through. The first 7 are easy enough to get through BUT on the last cavern you MUST have 5 dynamite and 1 jewel.
Tip: for those who are not good at the game (like myself) press and hold the "Start" button goto the game options and put on rewind, infinite lives and infinite time. With infinite time on you don't have to worry about the door closing after 60 seconds after hitting the pressure plate to open it.
You can also save the game anywhere so if you feel you might make a mistake and can't rewind back just keep frequently saving at the start of each stage over the 3 different save slots.
Also for those who got to the last level like myself and can't proceed any further I highly recommend starting a new game, but don't worry there is a way to skip the first 3 caverns if your fast enough. (video reference below/ speedrun video)
Cavern 1 skip: Quickly dig downwards a little and then to your right once you fall out jump to your right and kill the little goomba enemy type creature, if done correctly you will skip cavern 1. No room for error on this skip but with the rewind ability its very easy to try over and over again.
Cavern 2 skip: Immediately as the level starts run right and dig through the wall, you need to collect the rocks and then quickly jump over and collect the ladder. NO room for error, but again with the rewind ability you can try and try again.
Cavern 3: As soon as the level start run to your left and kill the ghoul as fast as possible and then hit the roof and hit the mushroom, run to the left a little and spawn another ghoul and kill it will under the effect of the mushroom. Little room for error but with the rewind it is doable.
Don't worry in cavern 4 - 7 you will be able to find everything you need to complete the last level. In cavern 4 there are "caves" that have loads of each item such as ladders and dynamite.
For those who haven't played through cavern 1 - 3 DON'T skip them as it will not count towards the achievement (thank you to Pyro Fool for confirming this)
Credit to Gurk Gamer for this video. This is a full walkthrough of the game with no skips.
I used this video below to find the fastest way to complete each stage and was able to complete the game in under 30 minutes.
Credit to PotatoHandle for this speedrun he uploaded of Digger T. Rock and also for explaining the cavern skips in the comment section.
**I'm really bad about explaining where to go in these types of games thats why I used Video references rather than written ones**