On the Skills page from the pause menu, you can choose to upgrade your skills/powers. There are three categories of skills available to upgrade - combat, biotics and tech. For this achievement, you have to upgrade one skill in each of these three categories to it's maximum Rank 6. You gain skill points from levelling up by completing missions and gaining XP.
Now, note. If you highlight a skill, on the right hand side of the screen, underneath the name of the skil and above the skill's description blurb, it will either say [Category] 'Power' or 'Passive' (e.g. Combat Power, Biotic Passive, etc). The skills you upgrade to level 6 MUST be a 'Power' skill, NOT a 'Passive' skill.
Upgrade one 'Power' skill to level 6 in each of the three categories, and the achievement is yours!