Here is the full list of all 65 Bejeweled 3 achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Collect 15 artifacts in Diamond Mine Mode
Clear 150 Hypercubes
Line up 6 Gems in a row
Clear 150 Star Gems
Destroy 60 gems in a single move
Score 100,000 points in Diamond Mine Mode
Score 300,000 points in Diamond Mine Mode
Score 500,000 points in Diamond Mine Mode
Collect 5 artifacts in Diamond Mine Mode
Collect 8 artifacts in Diamond Mine Mode
Collect 12 artifacts in Diamond Mine Mode
Clear 400 Flame Gems
Clear 25 Hypercubes
Score 100,000 points in Poker Mode
Clear 25 Star Gems
Finish a Classic game with a score over 150,000
Finish a Classic game with a score over 300,000
Finish a Classic game with a score over 500,000
Reach level 10 in Classic Mode
Destroy 50 gems in a single move
Clear 50 Flame Gems
Finish a Classic game with a score over 50,000
Destroy 30 gems in a single move
Destroy 40 gems in a single move
Score over 20,000 points during a Last Hurrah in Lightning Mode
Score over 30,000 points during a Last Hurrah in Lightning Mode
Score over 40,000 points during a Last Hurrah in Lightning Mode
Score 100,000 points in Lightning Mode
Clear 1400 Flame Gems
Clear 3400 Flame Gems
Clear 550 Star Gems
Clear 1300 Star Gems
Clear 550 Hypercubes
Clear 1300 Hypercubes
Score over 60,000 points during a Last Hurrah in Lightning Mode
Score 300,000 points in Lightning Mode
Score 500,000 points in Lightning Mode
Score 750,000 points in Lightning Mode
Score 300,000 points in Poker Mode
Score 500,000 points in Poker Mode
Score 750,000 points in Poker Mode
Get 10 flushes in Poker Mode
Get 30 flushes in Poker Mode
Get 60 flushes in Poker Mode
Get 100 flushes in Poker Mode
Score 100,000 points in Ice Storm Mode
Score 300,000 points in Ice Storm Mode
Score 500,000 points in Ice Storm Mode
Score 750,000 points in Ice Storm Mode
Get a 5x column combo in Ice Storm Mode
Get a 8x column combo in Ice Storm Mode
Get a 12x column combo in Ice Storm Mode
Get a 15x column combo in Ice Storm Mode
Score 750,000 points in Diamond Mine Mode
Score 100,000 points in Butterflies Mode
Score 300,000 points in Butterflies Mode
Score 500,000 points in Butterflies Mode
Score 750,000 points in Butterflies Mode
Collect 4 butterflies in a single move
Collect 6 butterflies in a single move
Collect 8 butterflies in a single move
Collect 10 butterflies in a single move
Complete Quest Mode
Match two Hypercubes together
Score 300,000 points in Poker, Butterflies, Ice Storm and Diamond Mine