This must be done together. Meaning once you win 20 tag battles, you must win 20 solo battles and vice versa or in any order, but you must not lose a single match, even after you win your 20 of whichever mode, until the achievement unlocks. What this means, is that if there is a boosting session set up for this, in order for 4 people to get this achievement, it should take about 4 hours, as each match is 3 minutes long.
Quick Formula. Team 1 = Players A & B. Team 2 = Players X & Y. A & B win 20 tags against X & Y. Then Player A goes solo against Player X, and Player B against Player Y for 20 solo matches. Afterwards, achievement unlocks for A & B, and then they reverse roles with Players X & Y.
There is an idle timeout, so if this is being boosted, the other team must at least be moving so as not to be disconnected from the match.
The score is based on total digging, amount of treasures you pick up, by digging through the boulders (the round shapes), the bonus star blocks, and finding that blue guy that sometimes hides sleeping as you're dig through blocks.
Dying makes you lose 10,000 points and also gives points to the others.
It took me 3 hours to get this achievement as well as the other MP achievements, which can be obtained while working towards this one. 2 players can work for this at a time, with 20 matches at 3 minutes each, tag and solo, for a total of 40 matches.
80 matches need to be won total between 4 players for the achievement to unlock for everyone involved in a 4-player boost.
This is a very tough "good faith" based achievement, as 2 players need to unlock it before the other 2.