Two stepper one by one
I looked into the source of the AccelStepper library here, which may be your library or one similar to it. The function runSpeedToPosition() does not block until the desired position is reached. Instead inside the function you see code that executes a step, when the right time (according to millis()), calculated through the speed, is reached, else it will return false. You are supposed to call this function very often while the motor moves. This enables you to drive more than one motor simultaneously with different speeds.

Since you don't want to drive both motors at the same time, you have to loop, until the first motor have reached the desired position; then doing the same with the second motor. Try something like this:

void PatternToBeLooped_For_Cycle1()
{
  int count = 0;
  for (count == 0; count &lt;= 5; count ++)
  {
    checkStepper1_For_DT(stepper1);
    while(stepper1.currentPosition() != stepper1.targetPosition()) stepper1.runSpeedToPosition();
  }

  checkStepper2_For_360(stepper2);
  while(stepper2.currentPosition() != stepper2.targetPosition()) stepper2.runSpeedToPosition();
}


Note: With this change the function PatternToBeLooped_For_Cycle1() blocks the execution of the loop function, until the motors have done their movement. To avoid this you can use an if-statement, which executes the code for stepper1 or stepper2 depending on the millis() function. This works the same way as the BlinkWithoutDelay example in the Arduino IDE.