Here is the full list of all 34 Reverse x Reverse achievements.
Clear World 3.
Clear World 2.
Clear World 1 (1-8).
Clear Stage 1-1.
Obtain S ranks or better on all World 1 stages up to Stage 8.
Clear Stage 1-9.
Obtain S ranks or better on all World 2 stages up to Stage 8.
Clear Stage 2-9.
Obtain S ranks or better on all World 3 stages up to Stage 8.
Clear Stage 3-9.
Clear World 4.
Obtain S ranks or better on all World 4 stages up to Stage 8.
Clear Stage 4-9.
Clear World 5.
Obtain S ranks or better on all World 5 stages up to Stage 8.
Clear Stage 5-9.
Clear World 6.
Obtain S ranks or better on all World 6 stages up to Stage 8.
Clear Stage 6-9.
Clear World 7.
Obtain S ranks or better on all World 7 stages up to Stage 8.
Clear Stage 7-9.
Clear World 8.
Obtain S ranks or better on all World 8 stages up to Stage 8.
Clear Stage 8-9.
Clear World 9.
Obtain S ranks or better on all World 9 stages up to Stage 8.
Clear Stage 9-9.
Beat up to Stage 7-8 within 150 minutes.
Beat up to Stage 7-8 within 80 minutes.
Clear all stages up through World 7.
Max out your collected Data.
Make a total of 1,000 stage attempts.
Obtain S ranks or better on all stages up to World 9.