The achievements for Michael Phelps: Push the Limit have been released. However, I must say that they look very intimidating as the majority of achievements are of 70G or higher. You must really push your limits to even get any of these achievements! So, prepare in advance by going through the achievements list and learn what you need to do to get those points.

Achievements

There are 15 achievements with a total of 1000 points.

First Finish 70G
Awarded for finishing your first race.

Globe Trotter 90G
Awarded for finishing a race in all the stadiums in career mode.

Season 2 Promotion 60G
A title awarded when you are promoted from Season 1 to Season 2.

Season 3 Promotion 70G
A title awarded when you are promoted from Season 2 to Season 3.

Backstroke Winner 70G
Awarded for winning a Backstroke race in career mode.

Breaststroke Winner 70G
Awarded for winning a Breaststroke race in career mode.

Butterfly Winner 70G
Awarded for winning a Butterfly race in career mode.

Front Crawl Winner 70G
Awarded for winning a Front Crawl race in career mode.

Hair Trigger 10G
Awarded for Jumping the Gun in a career race.

Optimum Dive 70G
Awarded for achieving an Optimum Dive in any race.

Optimum Turn 70G
Awarded for achieving an Optimum Turn in any race.

Optimum Finish 70G
Awarded by achieving a Good Reach in any race.

Pool Legend 100G
A title awarded when you complete Season 3 in Career Mode. 

Annual Games Debut 90G
A title awarded when you play for the first time in the Annual Games.

Hyped Up 20G
A title awarded when you max out the pre-race crowd excitement meter.

Source: Xbox360achievements