Your controller is made for a Bipolar stepper, which has two field coils, hence 4 wires. The motor with 8 leads is a Universal type, which has 4 coils, 8 wires. You should be able to connect the center pairs to each other. Typically those wires are striped, and if you count the wires 1 - 8, you would connect 3 to 4 and 5 to 6. You first need to confirm the pairs with a multimeter, identify the 4 pairs that show resistence and note the ohms. By connecting the two center pairs, you're converting it to Bipolar. After connecting the pairs, the 2 remaining pairs should have roughly twice the resistance value you read from the individual pairs.
All bets are off about whether or not you let the magic smoke out of your h-bridge!