Tunnel through the dirt, corner the creatures lurking underground, and pump them until they pop — keep clearing waves as the burrows fill up (three creatures, then four, then five from wave 3 on) and every wave makes them faster.
Swipe up/down/left/right to dig and move. The first row is sky; everything below starts as dirt. You can move freely through tunnels you've already dug; entering a dirt cell digs it open. Tap on a monster that is in a cell directly adjacent to you to pump it once — four pumps in a row pop it for points. If you stop pumping a monster, it slowly deflates back. Touching an un-inflated monster costs a life. Clear all monsters on the board to advance with a faster wave.
Your miner never stops in open ground: after a swipe it keeps going, digging as it goes, until it reaches the edge of the board or a creature is in the next cell. You don't need to stand still to attack, though. Tap a creature in any cell directly beside the cell your miner is in or passing through — even while he runs past it — and the pump lands and plants him at that cell's centre so he doesn't run on into trouble; swipe again to set off. Swiping straight toward a creature also halts you in the cell next to it. Pump at once: a creature that comes within about six-tenths of a cell of you costs a life, and standing in its way does not stop it.
Deeper kills score more: a pop is worth 100 points plus 20 for every row of depth, so a creature popped on row 11 is worth 320 against 180 on row 4 — almost double for the same four pumps. When a creature wanders to the bottom of the board, tunnel down to meet it instead of luring it up.
Don't over-dig early. Creatures cannot dig — they only travel through open tunnel — so every cell you cut becomes a path for them, and each wave adds another 6% of their starting speed. From wave 12 they are faster than your miner (about 4.65 cells per second against 4.5), so a straight run down a long tunnel stops being an escape, and from wave 3 on there are always five of them. Leave intact dirt walls between yourself and far-side creatures; one sealed off by dirt cannot reach you at all.
A single pump is a lifesaver. The moment you pump a creature it freezes where it stands and becomes harmless — it cannot take a life while any air is in it. Each pump holds for 0.55 seconds before the creature shrinks back one step, so keep pumping faster than that and the fourth pump pops it, while a single pump buys about half a second to swipe away. You still can't walk into the cell an inflated creature occupies, so escape down another tunnel, and remember it starts chasing again once it has fully deflated.