Block hexes one at a time to corner the cat before it reaches the edge of the board.
Tap any open hex to fill it with a block. After each tap the cat moves one step toward the nearest edge of the board, choosing the shortest path. Surround the cat completely (all six neighbors blocked or off-board) before it escapes to win the level. Each new level starts with fewer pre-placed blocks, making the cat harder to catch.
Don't chase the cat — anticipate it. Each turn the cat picks the shortest path to ANY edge, not just the nearest one in your face. Look at the whole board and identify which edge the cat can reach in the fewest steps, then block the choke point that funnels it there.
Build walls before they're needed. A single block in front of the cat just delays one move while opening another path. Instead, place blocks two or three hexes ahead in the direction the cat is heading, building a longer wall so when the cat arrives the trap is already in place.
Use the existing scattered blocks as anchors. Pre-placed blocks are free walls you didn't have to spend a turn on. Look for clusters or near-clusters and your job becomes 'extend this short wall into a full enclosure' instead of building from nothing.
The edge is always the cat's friend — corners are yours. The hex grid has more escape paths near the middle and fewer near the corners. If you can steer the cat into a corner region with two existing blocks nearby, you can often close it off with just 2–3 more taps.