Achieve means to complete or accomplish a task or goal successfully. A team works together to achieve more than each member of the team could do individually.
You cleave something when you split it along a natural grain by hitting it with a forceful blow. The man in the picture has cleaved some wood.
A cleaver is a type of knife with a large, rectangular blade. It is mainly used to cut through bone or other hard foods, but can also be used to dice food and to crush things like garlic.
Eaves are the part of a roof that slightly overhangs the walls of the house. Eaves protect the house from weather. A very wide eave would be called a verandah.
You grieve when you feel very sad for losing someone or something that you loved. Another word for grieve is mourn.
You heave when you put a lot of effort into pulling or raising something. The sailor in the picture is heaving a rope.
You retrieve something when you get it from somewhere it shouldn't be, and return it. For example you might retrieve a lost toy from your yard. The dog in the picture is retrieving a bone.
A sleeve is the part of a garment that covers your arm or part of your arm. Sleeves can be short, as on a t-shirt or so long they go past the end of your fingers.