I done it by overriding the write() method. Here is the code.

class AbcCrmLead(models.Model):     
    _inherit = 'crm.lead' 
    @api.multi
    def write(self, values):
        result = super(AbcCrmLead, self).write(values)
        for record in self:
            if not record.partner_id:
                raise UserError(_('Customer is required'))
            if not record.mobile:
                raise UserError(_('Mobile is required'))
            if record.stage_id.need_quotation and record.sale_number <= 0:
                raise UserError(_('Opportunity with No Quotation can\'t be moved to %s stage. Please add quotation(s) to move to next stage.' % record.stage_id.name))
        return result

The issue was when creating new opportunity from Kanban Quick Create Form. So I inherited the Kanban Quick Create Form and added required fields. 

<?xml version="1.0" encoding="UTF-8" ?>
<odoo>
    <record id="abc_quick_create_opportunity_form" model="ir.ui.view">
        <field name="name">abc.crm.lead.form.quick_create</field>
        <field name="model">crm.lead</field>
        <field name="inherit_id" ref="crm.quick_create_opportunity_form"/>
        <field name="arch" type="xml">
            <xpath expr="//field[@name='partner_id']" position="attributes">
                <attribute name="required">1</attribute>
            </xpath>
            <xpath expr="//field[@name='partner_id']" position="after">
                <field name="mobile" required="1"/>
                <field name="date_deadline" required="1"/>
                <field name="user_id" required="1"/>
                <field name="team_id" required="1"/>
            </xpath>
            <xpath expr="//field[@name='planned_revenue']" position="attributes">
                <attribute name="invisible">1</attribute>
            </xpath>
            <xpath expr="//field[@name='priority']" position="attributes">
                <attribute name="invisible">1</attribute>
            </xpath>
        </field>
    </record>
</odoo>

Now all validation is working by drag and drop from kanabn view, changing stage from form view.