Wall of Text:
First, the disclaimer: Unless I have missed something, which I doubt, most of the sets you will see after levels 1 and 2 cannot be resolved without guessing at some point. Sometimes, and more commonly as the levels increase, you will be faced with sets that are impossible to even get started on without a fairly low-odds guess.
That said, none of the guesses are completely unguided, and the first two levels are typically completely solvable. The general idea relies on the fact that you do not need to expose anything but 2s or 3s to max your reward and clear a board, so the 'value' of flipping a square with a 1 is essentially identical to the value of flipping a Voltorb.
The way this works is to render some rows/columns 'dead', in the sense that none of the squares on them will increase your ability to win.
Thus, at the start, especially on early sets, you will be faced with at least one row that is either dead or completely safe. Dead rows (without having flipped anything on them yet) are rows where the row/column numbers total to 5 (i.e. 4 total/1 voltorb, 3/2, 2/3, and so forth). Safe rows are obvious (no voltorbs). A 5 total/0 voltorb row is essentially dead, but it takes less work to flip the whole thing than it does to mark it as dead so you might as well flip it.
So, to start with, mark any row that is dead with whatever memo you like, and you can safely ignore that row/column for the rest of the game. This will leave you with either a row/column of flipped squares or one/two dead rows. In the former case, you generally have a better shot at winning than in the latter.
In the former case, you will hopefully have flipped a 2 or 3 (or, if you're really lucky, multiples/both). Any row/column in which you have flipped a 2 or a 3 needs to be re-checked to see if there is any way that row/column can contain another 2 or 3 - if it cannot, it is dead. So, for example, if you flip a 3 on a 6/1, that row needs to get 3 more to reach the total, and it needs a Voltorb, in 4 remaining squares - so it is dead, because it must be 1/1/1/Voltorb. Likewise, a 2 on a 5/1 renders that row dead. A 2 on a 6/1 does not help, and so forth.
In the latter case, and/or if you flipped a 2/3 but it didn't render a row dead, you need to guess to get started. The highest probability guesses are where high-total/low-voltorb rows intersect with high-total/low-voltorb columns (a 7/1 intersecting with a 9/1, for example). None of these guesses will ever be perfect, which is where the frustration comes in - you will flip Voltorbs on your first flip sometimes, and it will piss you off.
This will generally get you a sufficient number of flips on most sets that you wont be reset to a lower level (you get reset to Level X where X is the number of squares you flipped until you flip more than your current level). On later levels, you will typically end up faced with guesses midway through the game and very late.
In some cases, you can further narrow guesses down by figuring out if a row/column needs, say, a 3 somewhere but the column/row you are planning on intersecting it on cannot work with a 3. I am not, however, sold on how effective this is given the time it took me at least - if you aren't good at mental arithmetic, you should probably just ignore this until later levels. Getting reset to level 1 from 2 isn't a big deal, but from level 6 it is.
This will relatively consistently allow you to get to levels 5-6, where the coin winnings are sufficient to make quick progress towards high coin totals.
One thing to avoid is falling into the trap of treating Voltorbs identically to 1's - you will still run into cases where you can establish that a given square must be a Voltorb, and it is worth checking if that covers all the Voltorbs on the intersecting rows/columns - but this is quite rare.
One thing I am not sure about is the efficacy of guessing based on intersections of high totals, or intersections of low Voltorbs - the general rule of thumb I ended up following was to guess at intersections of low Voltorbs when I was at risk of resetting to a lower level, and to guess at intersections of high totals in all other cases.
If anything above needs clarification I'll try.