Enum Constants for Convert Units
I'm not at all sold on TRANSFORM being part of your enum. The API for this enum lets you make nonsense calls like WORLD.from(WORLD).to(TRANSFORM). Always try to prevent invalid use of your APIs. I'm not really sure why you wouldn't use a naive approach like two static methods Transformer.worldToScreen(Vector2) and Transformer.screenToWorld(Vector2). Are you anticipating needing additional conversions later?

If you're really hankering for a fluent API for some reason, you could do Transform.value(Vector2D).from(Sizes).to(Sizes). You can control the return types to prevent at least some of the possible errors, but there are still some invalid calls like Transform.value(...).from(WORLD).to(WORLD).

**** EDIT ****

Since you're interested in the fluent approach, here's something to get you started. Obviously it needs documentation and input checking. The DisplayType enum can either belong to Transform or it can be top-level, depending on your needs. Likewise, the two inner classes can easily be split out. 

As far as not instantiating objects, you can't really do a fluent API correctly without new objects. Do you have a real, demonstrated performance issue with creating new objects? Many people wrongly assume that object creation and garbage collection will be a big issue without testing.

If you really need to do this without new object instances, then your only good option as I see it is static methods. Your Sizes enum is too easy to use incorrectly.

public final class Transform {

    public static enum DisplayType {        
        SCREEN(new Vector2(800f, 480f)),
        WORLD(new Vector2(25.806f, 15.48f));

        private final Vector2 size;

        private DisplayType(final Vector2 size) {
            this.size = size;
        }
    }

    private Transform() {
        super();
    }

    public static From value(final Vector2 value) {
        return new From(value);
    }

    public static final class From {

        private final Vector2 value;

        From(final Vector2 value) {
            this.value = value;
        }

        public To from(final DisplayType sourceDisplayType) {
            return new To(this.value, sourceDisplayType);
        }
    }

    public static final class To {

        private final Vector2 value;
        private final DisplayType from;

        To(final Vector2 value, final DisplayType from) {
            this.value = value;
            this.from = from;
        }

        public Vector2 to(final DisplayType targetDisplayType) {
            /* TODO: Do math here */
            throw new UnsupportedOperationException();
        }
    }
}