The best way to level through PMU to take on harder dungeons is to have a good routine training dungeon you can tackle often or challenge with your friends.
Here is a good list of dungeons to try for all types of levels:
As it was specifically designed for such, the dungeon is good for any Level 1 Pokemon. Any level before 5 is good to train here, though.
Exbel Overworld/Tiny Grotto
Good for Level 5-10 Pokemon of any Type.
Level 10 Pokemon can train here until around level 16, unless you are weak to Water-Types.
Pokémon can train in the Bronze Chamber from Level 15+ to Level 20. Silver Chamber would be good for 20+ to Level 30. Gold Chamber is good for training Level 30+ to Level 40.
Level 25+ Pokemon can train here until about level 40-45. Good for Fire-Types. If you are weak to Flying-Types, Honeydrop Meadow is often a better option than Mt. Skylift.
Level 21+ Pokémon can train here until about level 50, but if your Pokemon is weak to Flying-Types, try training in HDM, then go to Southern Sea or Snowveil Den.
Level 35+ Pokémon can train here until about level 45. There is a small chance of getting past the boss but the floors are easy enough. If you are weak to Water-Types, try training in Mt. Skylift or Honeydrop Meadow.
Level 40-50 Pokémon can train here until about level 55-60. If your Pokemon is weak to Water-Types, try training in Mt. Skylift and then skip Southern Sea and train in Snowveil Den.
Level 50-60 Pokémon (depending on Type and Ability) can train here until about level 70-75. Beware of Discharge and Powder Snow spam.
Level 60-80+ Pokémon can train here to level 100, but the dungeon is full of Earthquake and Earth Power spammers.
Level 70-80+ Pokémon can train here to various levels depending on the chamber. In chambers with Beat Up, you can train to level 100 rather quickly. However, as better dungeons have come out, most will recommend a dungeon that you can bring supplies into.
Level 80+ Pokémon with Flash Fire or Water-Type Pokemon can train here to level 100 very quickly, and can even do so at a decent rate while Exp. Alling. Any Type that is strong against Fire-Types should be able to train here decently, but if you are using a Ground-type, consider bringing a Rock-type move for Charizard.
Often regarded as the best place for training, the dungeon is excellent for levels 70s and above (or 60s and above if you have type advantage). It provides large amounts of exp. points. It's filled with Grass- and Bug-types, so types weak to that may struggle, but many train regardless or use Family Items and find success.
Level 40-60 can train here until 70 or 75. There are a lot of supplies here that'll make it easy to train including Honeys. This is a moderately popular training spot.
Level 75+ Pokémon can train here until 100. Because it has many supplies, floors, and mobs of Pokemon in varying type, this has also become a good training location, but still less popular than Mysterious Jungle due how tedious it is to access it. A note of caution: If you are below 80, you should go in a training party.