This is what I have so far.
Plumbing - Jump on an enemy and kill it.
Grabber, Maku and Dan, Giant Face - Defeat the story bosses.
Fish Food -This is for pushing 20 enemies into the water on the 5th level (Metal Complex), it unlocked sometime after 20 enemies.
Smash - This is Smash 100 enemies,
Swordsman - The first mech you get on the 7th level (Contraband Tech), has a small gun and a large sword, get that mech to the end of the level, I found this easier to exit the mech, kill several enemies then pilot the mech to the next section to avoid losing the mech due to too much damage.
Pilot - On the same level with the Sword mech, 7th level (Contraband Tech), you come across the gun/missile mech, take this to the end of the level the same way as the swordsmech, can't be done on the same level.
Combustion - Burn 30 enemies, on the 5th level (Metal Complex), there is a propane tank near a checkpoint, I kept restarting, setting off the propane tank and pushing enemies into it. Fire can also be caused with the grenade launcher. I also observed sometimes setting fire to enemies with the Plasma Gun
Flytrap - In the level with the harpoon mech, 8th level (Bionic Gear), you will find a orange canister that when shot explodes into black expanding goop, if you explode one of these canisters when a Stalker (large four legged robot with sword tail) is standing near one it will expand and trap the stalker.
Harpoon FTW - Get the harpoon mech to the end of the level you find it on. 8th level (Bionic Gear)
Relic - On the last level (8th level (Bionic Gear)), there is a platforming waterfall section near the start, once at the top move to the far left and you can see a log leaning out over the edge, the relic is atop that section, standing near it activates the achievementhttp://steamcommunity.com/sharedfiles/filedetails/?id=97365325
Shake Shake - Catch a Stalkers missile and shake it about, it will grow in size and you'll get the achievement. This can only be done on the 8th level Bionic Gear. To catch the missile you need to be piloting the harpoon mech, you only get three chances to catch the missiles because Stalkers only have three missiles. - Thanks to Road for this one http://steamcommunity.com/sharedfiles/filedetails/?id=97496176
Hardboiled - Beat the last boss on Hard