It depends on what achievement you did. If you did an achievement based on a core stat (str, agi, int, wis, luck) then you might not notice the increase if your stat was already low, like sregi2 said.
If you did an achievement based on weapon crafting, it won't take effect unless you are wearing the weapon; again, you might not also notice the difference if your patk/matk with the weapon was low.
If you did an armor achievement, the stat increase is static, so it will add a passive % to whatever the stat was (Ex: Cloth armor 1-30 gives 3% elemental resists, or 3 resists. So if you had 20 resists b4 the achievement, you now get 23 resists, not 20 + (20*3%) resists.
If you did an accessory achievement, the bonus will also be static. Necklaces 1-30 for example would show up on your cast speed at x.xx + 3% cast speed. Rings increase crit and mcrit DAMAGE not rate, so if you did that, check your crit/mcrit dmg. It should have increased by .05 for each level of the achievement you completed.
If you did gem achievements, it will add static movespeed. (Ex: Gems 1-30 would get u 2.00 move speed, not 2% of whatever movespeed you had).
If you did the rare monsters or enchants achievements, you won't be able to tell from looking at your stats, b/c currently there is no shown measurement for exp/cp increase or double hit rate.
If you did trophies, the hp should be added to your hp bar.