Here is the full list of all 36 A Blast From The Past achievements.
Get a Perfect on any bonus round.
Kill 1000 Enemies.
Destroy 10 Formations.
Detonated 10 Nova bombs.
Destroy 1 Elite.
Reach Wave 5 without dying.
Power up your ship with 3 power stars.
Get Perfect on 50 bonus rounds.
Get Perfect on 500 bonus rounds.
Kill 10000 Enemies.
Kill 100000 Enemies.
Destroy 100 Formations.
Destroy 1000 Formations.
Ram 100 Enemies with your shield.
Ram 500 Enemies with your shield.
Ram 1000 Enemies with your shield.
Collect 100 power stars.
Collect 500 power stars.
Collect 1000 power stars.
Score at least a million points.
Detonated 100 Nova bombs.
Detonated 1000 Nova bombs.
Get 5 Perfect bonus rounds in a row.
Reach Wave 50.
Reach Wave 100.
Destroy 10 Elites.
Destroy 100 Eliltes.
Score at least 5 million points.
Get a Perfect on any bonus round with no powerup.
Get 49 out of 50 kills on any bonus round.
Destroy an entire wave before an enemy settles.
Destroy 5 Space Snakes.
Destroy 50 Space Snakes.
Destroy 500 Space Snakes.
Reach Wave 10 without dying.
Reach Wave 20 without dying.