My high score at the moment: 86.
Personal tutorial:
At first, you need to figure out what relationships between these tiles are: -2 meet -1=0; -1 meet -2=+4; -2 meet+2=-2; +1 meet -1=+1; -2 meet +1=+3; -1 meet +3=+1; 0 meet+1=+3(it need -2 near around).
Tips you need to learn after you remember all relationships:
1. you need to turn -1 into +2 as fast as possible
2. you need to move +1 near -2 as more as possible
3. you need to use +4 to help you move rows or columns when one column of layers almost fill up
4. don't move the cursor from -2 to -1 unless you need 2.
5. you can't move +1 after it turn into +3 so be careful
6. 0,+1, -1, +4 can be moved but they will cost steps in one turn too
7. On the opposite, -2, +2,+3 can't be moved.
Good luck! Hope this tutorial can help you a bit.